U.S. patent number 10,646,445 [Application Number 15/690,014] was granted by the patent office on 2020-05-12 for analysis compensation including segmented signals converted into signal processing parameters for describing a portion of total error.
This patent grant is currently assigned to Ascensia Diabetes Care Holdings AG. The grantee listed for this patent is Ascensia Diabetes Care Holdings AG. Invention is credited to Huan-Ping Wu.
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United States Patent |
10,646,445 |
Wu |
May 12, 2020 |
Analysis compensation including segmented signals converted into
signal processing parameters for describing a portion of total
error
Abstract
A biosensor system determines analyte concentration from an
output signal generated from a light-identifiable species or a
redox reaction of the analyte. The biosensor system compensates at
least 50% of the total error in the output signal with a primary
function and may compensate a portion of the residual error with at
least one residual function. An SSP function may serve as the
primary function, first residual function, or second residual
function. Preferably, when the SSP function serves as the first
residual function, the SSP function compensates at least 50% of the
residual error remaining after primary compensation. Preferably,
when the SSP function serves as the second residual function, the
SSP function compensates at least 50% of the residual error
remaining after primary and first residual compensation. The error
compensation provided by the primary, first residual, and second
residual functions may be adjusted with function weighing
coefficients.
Inventors: |
Wu; Huan-Ping (Granger,
IN) |
Applicant: |
Name |
City |
State |
Country |
Type |
Ascensia Diabetes Care Holdings AG |
Basel |
N/A |
CH |
|
|
Assignee: |
Ascensia Diabetes Care Holdings
AG (Basel, CH)
|
Family
ID: |
47881000 |
Appl.
No.: |
15/690,014 |
Filed: |
August 29, 2017 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20170360712 A1 |
Dec 21, 2017 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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13623654 |
Sep 20, 2012 |
9775806 |
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61537145 |
Sep 21, 2011 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
A61K
9/19 (20130101); G01N 27/3274 (20130101); A61K
47/26 (20130101); A61K 31/198 (20130101); A61K
9/0019 (20130101) |
Current International
Class: |
A61K
9/19 (20060101); A61K 9/00 (20060101); G01N
27/327 (20060101); A61K 31/198 (20060101); A61K
47/26 (20060101) |
References Cited
[Referenced By]
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Other References
European Patent Office, International. Search Report and Written
Opinion of International Searching Authority for PCT/US2006/028013,
dated Dec. 6, 2006 (16 pages). cited by applicant .
European Patent Office, International Search Report and Written
Opinion of International Searching Authority for PCT/US2007/068320,
dated Oct. 19, 2007 (14 pages). cited by applicant .
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Opinion of International Searching Authority for PCT/US2008/085768,
dated Sep. 29, 2009 (16 pages). cited by applicant .
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dated Jun. 20, 2011 (11 pages). cited by applicant .
European Patent Office, International Search Report and Written
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dated Feb. 25, 2013 (17 pages). cited by applicant .
Gunasingham, et al.; "Pulsed amperometric detection of glucose
using a mediated enzyme electrode"; Journal of Electroanalytical
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.
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|
Primary Examiner: Vanni; G Steven
Attorney, Agent or Firm: Nixon Peabody LLP
Parent Case Text
REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. application Ser. No.
13/623,654, filed Sep. 20, 2012, and titled "Analysis Compensation
Including Segmented Signals," now allowed, which claims the benefit
of U.S. Provisional Application No. 61/537,145, filed Sep. 21,
2011, and titled "Analysis Compensation Including Segmented Signal
Processing", each of which is hereby incorporated by reference in
its entirety.
Claims
What is claimed is:
1. A method of operating a biosensor system, the method comprising:
providing a biosensor system in the form of an analytical
instrument including a measurement device having electrical
circuitry communicatively coupled to a processor, a storage medium,
a signal generator, and a sensor interface, the processor having
instructions and data stored in the storage medium, and a test
sensor having a base and a sample interface, the base forming a
reservoir and a channel with an opening, the reservoir being in
electrical or optical communication with the measurement device,
the test sensor having a chemical reagent capable of reacting with
an analyte in a biological fluid sample; receiving the biological
fluid sample in the opening of the reservoir, the biological fluid
sample flowing through the channel to fill at least in part the
reservoir of the test sensor, the biological fluid sample including
the analyte, the analyte in the biological fluid sample reacting in
a chemical reaction with the chemical reagent in the reservoir; in
response to the chemical reaction in the reservoir, generating an
input signal from the signal generator for excitation of a chemical
reaction product during an excitation period, the input signal
including at least one excitation having a time period with an
end-point; transmitting the input signal by the sensor interface to
the sample interface for applying the input signal to the
biological fluid sample; in response to the input signal and the
concentration of the analyte in the biological fluid sample,
generating, by the processor, one or more output signals from the
test sensor; segmenting, by the processor, the one or more output
signals during the excitation period into at least two segments
with a regular or irregular segmenting interval, each segment
including point readings obtained before the end-point of the input
signal during the excitation period; converting, by the processor,
the at least two segments into at least two signal processing
parameters, wherein the signal processing parameters describe a
portion of a total error in the one or more output signals;
determining, by the processor, a segmented signal processing
function from the signal processing parameters; using, by the
processor, a predetermined reference correlation to relate the one
or more output signals to a plurality of known sample analyte
concentrations; in response to the predetermined reference
correlation, using, by the processor, a conversion function to
convert the one or more output signals into one known sample
analyte concentration of the plurality of known sample analyte
concentrations; determining, by the processor, a compensated value
from the one or more output signals in response to the conversion
function and the segmented signal processing function; determining,
by the processor, the analyte concentration in the biological fluid
sample from the compensated value of the one or more output
signals; and outputting, by the processor, the analyte
concentration to one or more of a display, a remote receiver, or a
storage medium.
2. The method of claim 1, wherein the one or more output signals
are responsive to a concentration of a measurable species in the
biological fluid sample and the concentration of the measurable
species in the biological fluid sample is responsive to the
concentration of the analyte in the biological fluid sample.
3. The method of claim 2, wherein the concentration of the
measurable species in the biological fluid sample is responsive to
a chemical reaction between the analyte, an enzyme, and a mediator,
where the chemical reaction is the redox reaction.
4. The method of claim 2, wherein the measurable species is
light-identifiable.
5. The method of claim 1, further comprising continuously applying
the input signal to the sample until an analysis end-point is
reached.
6. The method of claim 5, further comprising measuring at least
three output signal values from the one or more output signals.
7. The method of claim 1, wherein the input signal is gated and the
excitation is applied until an intermediate analysis end-point is
reached.
8. The method of claim 7, further comprising measuring at least two
output signal values from the one or more output signals.
9. The method of claim 1, wherein the segmented signal processing
function is predetermined.
10. The method of claim 9, wherein the at least two signal
processing parameters are determined from the one or more output
signals with a parameter determining method selected from the group
consisting of averaging of signals within a segment, determining
ratios of the signal values from within a segment, determining
differentials of the signal values from within a segment,
determining time-based differentials, determining normalized
differentials, determining time-based normalized differentials,
determining one or more decay constants, and determining one or
more decay rates.
11. The method of claim 9, wherein the at least two signal
processing parameters are determined using a parameter determining
method selected from the group consisting of determining
differentials of the signal values from within a segment,
determining time-based differentials, determining normalized
differentials, and determining time-based normalized
differentials.
12. The method of claim 9, wherein the at least two signal
processing parameters are determined using a parameter determining
method selected from the group consisting of determining time-based
differentials and determining time-based normalized
differentials.
13. The method of claim 1, further comprising converting the one or
more output signals with the conversion function before applying
the segmented signal processing function.
14. The method of claim 1, wherein the analyte concentration in the
biological fluid sample determined from the compensated value
includes 30% less relative error than if the analyte concentration
in the biological fluid sample were determined from the one or more
output signals and the conversion function without the segmented
signal processing function.
15. The method of claim 14, wherein the analyte concentration in
the biological fluid sample determined from the compensated value
includes 50% less relative error than if the analyte concentration
in the biological fluid sample were determined from the one or more
output signals and the conversion function without the segmented
signal processing function.
16. The method of claim 13, wherein determining the compensated
value from the one or more output signals in response to the
conversion function and the segmented signal processing function
further comprises determining the compensated value from the one or
more output signals in response to a primary function, the
segmented signal processing function not being the primary
function, the primary function describing a major error in the one
or more output signals and relating uncompensated output values and
error contributors, the major error being attributable to one or
more major error contributors selected from a group consisting of
temperature, hematocrit, and hemoglobin.
17. The method of claim 16, wherein error described by the
segmented signal processing function is substantially different
than error described by the primary function.
18. The method of claim 16, further comprising modifying the
segmented signal processing function and the primary function with
function weighing coefficients.
19. A biosensor system for determining an analyte concentration in
a biological fluid sample, the biosensor system being an optical
system or an electrochemical system, the biosensor system
comprising: a test sensor having a base and a sample interface, the
base forming a reservoir and a channel with an opening, the opening
being configured to receive the biological fluid sample and to
allow the biological fluid sample to flow through the channel to
fill at least in part the reservoir, the reservoir being in
electrical or optical communication with the measurement device,
the test sensor having a chemical reagent reacting in a chemical
reaction with the analyte in the biological fluid sample when the
biological fluid sample is received in the reservoir; a measurement
device in electrical or optical communication with the reservoir,
the measurement device having electrical circuitry communicatively
coupled to a processor, a storage medium, a signal generator, and a
sensor interface, the processor having instructions and data stored
in the storage medium, the instructions configured such that when
executed by the processor the system is enabled so that: in
response to the chemical reaction in the reservoir, the signal
generator applies an electrical or optical input signal to the
sensor interface, the input signal including at least one
excitation having a time period with an end-point, the input signal
is transmitted by the sensor interface to the sample interface for
applying the input signal to the biological fluid sample, in
response to the input signal and to the concentration of the
analyte in the biological fluid sample, the processor generates one
or more output signals from the test sensor during an excitation
period, the processor segments the one or more output signals
during the excitation period of the one or more output signals into
at least two segments with a regular or irregular segmenting
interval, each segment including point readings obtained before the
end-point of the input signal during the excitation period; the
processor converts the one or more output signals of the at least
two segments into at least two signal processing parameters,
wherein the segmented signal processing parameters describe a
portion of a total error in the one or more output signals; the
processor determines a segmented signal processing function from
the signal processing parameters; the processor uses a
predetermined reference correlation to relate the one or more
output signals to a plurality of known sample analyte
concentrations; in response to the predetermined reference
correlation, the processor uses a conversion function to convert
the one or more output signals into one known sample analyte
concentration of the plurality of known sample analyte
concentrations; the processor determines a compensated value from
the one or more output signals in response to the conversion
function and the segmented signal processing function; the
processor determines the analyte concentration in the biological
fluid sample from the compensated value of the one or more output
signals; and the processor outputs the analyte concentration to one
or more of a display, a remote receiver, or a storage medium.
20. The biosensor system of claim 19, wherein the processor
compensates at least 50% of the total error in the one or more
output signals with a primary function, the primary function
describing a major error in the one or more output signals and
relating uncompensated output values and error contributors, the
major error being attributable to one or more major error
contributors selected from a group consisting of temperature,
hematocrit, and hemoglobin; and if the primary function is not the
predetermined segmented signal processing function, the processor
compensates at least 5% of the remaining error in the one or more
output signals with the predetermined segmented signal processing
function.
21. A method of operating a biosensor system for determining an
analyte concentration in a biological fluid sample, the biosensor
system being an optical sensor system or an electrochemical sensor
system, the biosensor system including a measurement device and a
test sensor, the measurement device having a processor, the test
sensor being in electrical or optical communication with a
reservoir, the method using the processor in performing steps
comprising: receiving the biological fluid sample in the reservoir
of the test sensor, the biological fluid sample including the
analyte; applying an input signal to the biological fluid sample,
the input signal including an excitation; generating during an
excitation period, via the biosensor system, an output signal
responsive to the input signal and further responsive to the
concentration of the analyte, the output signal being one or more
of a light-generated output signal in response to a
light-identifiable species and an electrical output signal
generated by a redox reaction; segmenting the output signal during
the excitation period of the excitation into at least two segments,
each segment including point readings obtained before an end-point
of the excitation period; converting the at least two segments into
at least two signal processing parameters, the signal processing
parameters describing a portion of a total error in the output
signal; determining a segmented signal processing function from the
signal processing parameters; determining a compensated value from
the output signal in response to the segmented signal processing
function; determining the analyte concentration from the
compensated value of the output signal; and outputting the analyte
concentration to one or more of a display, a remote receiver, or a
storage medium.
Description
BACKGROUND
Biosensor systems provide an analysis of a biological fluid sample,
such as blood, serum, plasma, urine, saliva, interstitial, or
intracellular fluid. Typically, the systems include a measurement
device that analyzes a sample residing in a test sensor. The sample
usually is in liquid form and in addition to being a biological
fluid, may be the derivative of a biological fluid, such as an
extract, a dilution, a filtrate, or a reconstituted precipitate.
The analysis performed by the biosensor system determines the
presence and/or concentration of one or more analytes, such as
alcohol, glucose, uric acid, lactate, cholesterol, bilirubin, free
fatty acids, triglycerides, proteins, ketones, phenylalanine or
enzymes, in the biological fluid. The analysis may be useful in the
diagnosis and treatment of physiological abnormalities. For
example, a person with diabetes may use a biosensor system to
determine the glucose level in blood for adjustments to diet and/or
medication.
In blood samples including hemoglobin (Hb), the presence and/or
concentration of total hemoglobin and glycated hemoglobin (HbA1c)
may be determined. HbA1c (%-A1c) is a reflection of the state of
glucose control in diabetic patients, providing insight into the
average glucose control over the three months preceding the test.
For diabetic individuals, an accurate measurement of %-A1c assists
in the determination of the blood glucose level, as adjustments to
diet and/or medication are based on these levels.
Biosensor systems may be designed to analyze one or more analytes
and may use different volumes of biological fluids. Some systems
may analyze a single drop of blood, such as from 0.25-15
microliters (.mu.L) in volume. Biosensor systems may be implemented
using bench-top, portable, and like measurement devices. Portable
measurement devices may be hand-held and allow for the
identification and/or quantification of one or more analytes in a
sample. Examples of portable measurement systems include the
Elite.RTM. meters of Bayer HealthCare in Tarrytown, N.Y., while
examples of bench-top measurement systems include the
Electrochemical Workstation available from CH Instruments in
Austin, Tex.
Biosensor systems may use optical and/or electrochemical methods to
analyze the biological fluid. In some optical systems, the analyte
concentration is determined by measuring light that has interacted
with or been absorbed by a light-identifiable species, such as the
analyte or a reaction or product formed from a chemical indicator
reacting with the analyte. In other optical systems, a chemical
indicator fluoresces or emits light in response to the analyte when
illuminated by an excitation beam. The light may be converted into
an electrical output signal, such as current or potential, which
may be similarly processed to the output signal from an
electrochemical system. In either optical system, the system
measures and correlates the light with the analyte concentration of
the sample.
In light-absorption optical systems, the chemical indicator
produces a reaction product that absorbs light. A chemical
indicator such as tetrazolium along with an enzyme such as
diaphorase may be used. Tetrazolium usually forms formazan (a
chromagen) in response to the redox reaction of the analyte. An
incident input beam from a light source is directed toward the
sample. The light source may be a laser, a light emitting diode, or
the like. The incident beam may have a wavelength selected for
absorption by the reaction product. As the incident beam passes
through the sample, the reaction product absorbs a portion of the
incident beam, thus attenuating or reducing the intensity of the
incident beam. The incident beam may be reflected back from or
transmitted through the sample to a detector. The detector collects
and measures the attenuated incident beam (output signal). The
amount of light attenuated by the reaction product is an indication
of the analyte concentration in the sample.
In light-generated optical systems, the chemical detector
fluoresces or emits light in response to the analyte redox
reaction. A detector collects and measures the generated light
(output signal). The amount of light produced by the chemical
indicator is an indication of the analyte concentration in the
sample.
An example of an optical system using reflectance is a laminar flow
A1c system that determines the concentration of A1c hemoglobin in
blood. These systems use immunoassay chemistry where the blood is
introduced to the test sensor where it reacts with reagents and
then flows along a reagent membrane. When contacted by the blood,
A1c antibody coated color beads release and move along with the
blood sample to a detection zone 1. Because of the competition
between the A1c in the blood sample and an A1c peptide present in
detection zone 1 for the color beads, color beads not attached to
the A1c antibody are captured at zone 1 and are thus detected as
the A1c signal from the change in reflectance. The total hemoglobin
(THb) in the blood sample also is reacting with other blood
treatment reagents and moves downstream into detection zone 2,
where it is measured at a different wavelength. For determining the
concentration of A1c in the blood sample, the reflectance signal is
proportional to the A1c analyte concentration (%-A1c). For the THb
measurement, however, the reflectance in zone 2 is inversely
proportional to the THb (mg/dL) for the detection system.
In electrochemical systems, the analyte concentration is determined
from an electrical signal generated by an oxidation/reduction or
redox reaction of the analyte or a species responsive to the
analyte when an input signal is applied to the sample. The input
signal may be a potential or current and may be constant, variable,
or a combination thereof such as when an AC signal is applied with
a DC signal offset. The input signal may be applied as a single
pulse or in multiple pulses, sequences, or cycles. An enzyme or
similar species may be added to the sample to enhance the electron
transfer from a first species to a second species during the redox
reaction. The enzyme or similar species may react with a single
analyte, thus providing specificity to a portion of the generated
output signal. A mediator may be used to maintain the oxidation
state of the enzyme and/or assist with electron transfer from the
analyte to an electrode.
Electrochemical biosensor systems usually include a measurement
device having electrical contacts that connect with the electrical
conductors of the test sensor. The conductors may be made from
conductive materials, such as solid metals, metal pastes,
conductive carbon, conductive carbon pastes, conductive polymers,
and the like. The electrical conductors typically connect to
working, counter, reference, and/or other electrodes that extend
into a sample reservoir. One or more electrical conductors also may
extend into the sample reservoir to provide functionality not
provided by the electrodes.
The measurement device applies an input signal through the
electrical contacts to the electrical conductors of the test
sensor. The electrical conductors convey the input signal through
the electrodes into the sample present in the sample reservoir. The
redox reaction of the analyte generates an electrical output signal
in response to the input signal. The electrical output signal from
the test sensor may be a current (as generated by amperometry or
voltammetry), a potential (as generated by
potentiometry/galvanometry), or an accumulated charge (as generated
by coulometry). The measurement device may have the processing
capability to measure and correlate the output signal with the
presence and/or concentration of one or more analytes in the
sample.
In coulometry, a potential is applied to the sample to exhaustively
oxidize or reduce the analyte. A biosensor system using coulometry
is described in U.S. Pat. No. 6,120,676. In amperometry, an
electrical signal of constant potential (voltage) is applied to the
electrical conductors of the test sensor while the measured output
signal is a current. Biosensor systems using amperometry are
described in U.S. Pat. Nos. 5,620,579; 5,653,863; 6,153,069; and
6,413,411. In voltammetry, an electric signal of varying potential
is applied to a sample of biological fluid, while the measured
output is current. In gated amperometry and gated voltammetry,
pulsed inputs are used as described in WO 2007/013915 and WO
2007/040913, respectively.
Output signal values that are responsive to the analyte
concentration of the sample include those obtained from the
analytic input signal. Output signal values that are substantially
independent of values responsive to the analyte concentration of
the sample include values responsive to temperature and values
substantially responsive to interferents, such as the hematocrit or
acetaminophen content of a blood sample when the analyte is
glucose, for example. Output signals substantially not responsive
to analyte concentration may be referred to as secondary output
signals, as they are not primary output signals responsive to the
alteration of light by the analyte or analyte responsive indicator,
electrochemical redox reaction of the analyte, or analyte
responsive redox mediator. Secondary output signals may arise from
the sample or from other sources, such as a thermocouple.
In many biosensor systems, the test sensor may be adapted for use
outside, inside, or partially inside a living organism. When used
outside a living organism, a sample of the biological fluid may be
introduced into a sample reservoir in the test sensor. The test
sensor may be placed in the measurement device before, after, or
during the introduction of the sample for analysis. When inside or
partially inside a living organism, the test sensor may be
continually immersed in the sample or the sample may be
intermittently introduced to the test sensor. The test sensor may
include a reservoir that partially isolates a volume of the sample
or be open to the sample. When open, the test sensor may take the
form of a fiber or other structure placed in contact with the
biological fluid. Similarly, the sample may continuously flow
through the test sensor, such as for continuous monitoring, or be
interrupted, such as for intermittent monitoring, for analysis.
The measurement performance of a biosensor system is defined in
terms of accuracy and precision. Accuracy reflects the combined
effects of random and systematic error components. Systematic
error, or trueness, is the difference between the average value
determined from the biosensor system and one or more accepted
reference values for the analyte concentration of the biological
fluid. Trueness may be expressed in terms of mean bias, with larger
mean bias values representing lower trueness and thereby
contributing to less accuracy. Precision is the closeness of
agreement among multiple analyte readings in relation to a mean.
One or more error in the analysis contribute to the bias and/or
imprecision of the analyte concentration determined by the
biosensor system. A reduction in the analysis error of a biosensor
system therefore leads to an increase in accuracy and thus an
improvement in measurement performance.
Bias may be expressed in terms of "absolute bias" or "percent
bias". Absolute bias is the difference between the determined
concentration and the reference concentration, and may be expressed
in the units of the measurement, such as mg/dL, while percent bias
may be expressed as a percentage of the absolute bias value over
100 mg/dL or the reference analyte concentration of the sample. For
glucose concentrations less than 100 mg/dL, percent bias is defined
as (the absolute bias over 100 mg/dL)*100. For glucose
concentrations of 100 mg/dL and higher, percent bias is defined as
the absolute bias over the reference analyte concentration*100.
Accepted reference values for the analyte glucose in blood samples
may be obtained with a reference instrument, such as the YSI 2300
STAT PLUS.TM. available from YSI Inc., Yellow Springs, Ohio. Other
reference instruments and ways to determine percent bias may be
used for other analytes. For the %-A1c measurements, the error may
be expressed as either absolute bias or percent bias against the
%-A1c reference value for the therapeutic range of 4-12%. Accepted
reference values for the %-A1c in blood samples may be obtained
with a reference instrument, such as the Tosoh G7 instrument
available from Tosoh Corp, Japan.
Hematocrit bias refers to the average difference (systematic error)
between the reference glucose concentration obtained with a
reference instrument and experimental glucose readings obtained
from a biosensor system for samples containing differing hematocrit
levels. The difference between the reference and values obtained
from the system results from the varying hematocrit level between
specific blood samples and may be generally expressed as a
percentage by the following equation: %
Hct-Bias=100%.times.(G.sub.m-G.sub.ref)/G.sub.ref, where G.sub.m is
the determined glucose concentration at a specific hematocrit level
and G.sub.ref is the reference glucose concentration at a reference
hematocrit level. The larger the absolute value of the % Hct-bias,
the more the hematocrit level of the sample (expressed as % Hct,
the percentage of red blood cell volume/sample volume) is reducing
the accuracy of the determined glucose concentration.
For example, if blood samples containing identical glucose
concentrations, but having hematocrit levels of 20, 40, and 60%,
are analyzed, three different glucose concentrations will be
reported by a system based on one set of calibration constants
(slope and intercept of the 40% hematocrit containing blood sample,
for instance). Thus, even though the blood glucose concentrations
are the same, the system will report that the 20% hematocrit sample
contains more glucose than the 40% hematocrit sample, and that the
60% hematocrit sample contains less glucose than the 40% hematocrit
sample. "Hematocrit sensitivity" is an expression of the degree to
which changes in the hematocrit level of a sample affect the bias
values for an analysis. Hematocrit sensitivity may be defined as
the numerical values of the percent biases per percent hematocrit,
thus bias/%-bias per % Hct.
Biosensor systems may provide an output signal during the analysis
of the biological fluid including error from multiple error
sources. These error sources contribute to the total error, which
may be reflected in an abnormal output signal, such as when one or
more portions or the entire output signal is non-responsive or
improperly responsive to the analyte concentration of the
sample.
The total error in the output signal may originate from one or more
error contributors, such as the physical characteristics of the
sample, the environmental aspects of the sample, the operating
conditions of the system, the manufacturing variation between test
sensor lots, and the like. Physical characteristics of the sample
include hematocrit (red blood cell) concentration, interfering
substances, such as lipids and proteins, and the like. Interfering
substances include ascorbic acid, uric acid, acetaminophen, and the
like. Environmental aspects of the sample include temperature,
oxygen content of the air, and the like. Operating conditions of
the system include underfill conditions when the sample size is not
large enough, slow-filling of the sample, intermittent electrical
contact between the sample and one or more electrodes in the test
sensor, prior degradation of the reagents that interact with the
analyte, and the like. Manufacturing variations between test sensor
lots include changes in the amount and/or activity of the reagents,
changes in the electrode area and/or spacing, changes in the
electrical conductivity of the conductors and electrodes, and the
like. A test sensor lot is preferably made in a single
manufacturing run where lot-to-lot manufacturing variation is
substantially reduced or eliminated. Manufacturing variations also
may be introduced as the activity of the reagents changes or
degrades between the time the test sensor is manufactured and when
it is used for an analysis. There may be other contributors or a
combination of error contributors that cause error in the
analysis.
Percent bias, percent bias standard deviation, mean percent bias,
relative error, and hematocrit sensitivity are independent ways to
express the measurement performance of a biosensor system.
Additional ways may be used to express the measurement performance
of a biosensor system.
Percent bias is a representation of the accuracy of the biosensor
system in relation to a reference analyte concentration, while the
percent bias standard deviation reflects the accuracy of multiple
analyses, with regard to error arising from the physical
characteristics of the sample, the environmental aspects of the
sample, and the operating conditions of the system. Thus, a
decrease in percent bias standard deviation represents an increase
in the measurement performance of the biosensor system across
multiple analyses.
The mean may be determined for the percent biases determined from
multiple analyses using test sensors from a single lot to provide a
"mean percent bias" for the multiple analyses. The mean percent
bias may be determined for a single lot of test sensors by using a
subset of the lot, such as 100-140 test sensors, to analyze
multiple blood samples.
Relative error is a general expression of error that may be
expressed as .DELTA.G/G.sub.ref (relative
error)=(G.sub.calculated-G.sub.ref)/G.sub.ref=G.sub.calculated/G.sub.ref--
1; where .DELTA.G is the error present in the analysis determined
analyte concentration in relation to the reference analyte
concentration; G.sub.calculated is the analyte concentration
determined from the sample during the analysis; and G.sub.ref is
the analyte concentration of the sample as determined by a
reference instrument.
Increasing the measurement performance of the biosensor system by
reducing error from these or other sources means that more of the
analyte concentrations determined by the biosensor system may be
used for accurate therapy by the patient when blood glucose is
being monitored, for example. Additionally, the need to discard
test sensors and repeat the analysis by the patient also may be
reduced.
A test case is a collection of multiple analyses (data population)
arising under substantially the same testing conditions using test
sensors from the same lot. For example, determined analyte
concentration values have typically exhibited poorer measurement
performance for user self-testing than for health care professional
("HCP") testing and poorer measurement performance for HCP-testing
than for controlled environment testing. This difference in
measurement performance may be reflected in larger percent bias
standard deviations for analyte concentrations determined through
user self-testing than for analyte concentrations determined
through HCP-testing or through controlled environment testing. A
controlled environment is an environment where physical
characteristics and environmental aspects of the sample may be
controlled, preferably a laboratory setting. Thus, in a controlled
environment, hematocrit concentrations can be fixed and actual
sample temperatures can be known and compensated. In a HCP test
case, the operating condition error may be reduced or eliminated.
In a user self-testing test case, such as a clinical trial, the
determined analyte concentrations likely will include error from
all types of error sources.
Biosensor systems may have a single source of uncompensated output
values responsive to a redox or light-based reaction of the
analyte, such as the counter and working electrodes of an
electrochemical system. Biosensor systems also may have the
optional ability to determine or estimate temperature, such as with
one or more thermocouples or other means. In addition to these
systems, biosensor systems also may have the ability to generate
additional output values external to those from the analyte or from
a mediator responsive to the analyte. For example, in an
electrochemical test sensor, one or more electrical conductors also
may extend into the sample reservoir to provide functionality not
provided by the working and counter electrodes. Such conductors may
lack one or more of the working electrode reagents, such as the
mediator, thus allowing for the subtraction of a background
interferent signal from the working electrode signal.
Many biosensor systems include one or more methods to compensate
for error associated with an analysis, thus attempting to improve
the measurement performance of the biosensor system. Compensation
methods may increase the measurement performance of a biosensor
system by providing the biosensor system with the ability to
compensate for inaccurate analyses, thus increasing the accuracy
and/or precision of the concentration values obtained from the
system. However, these methods have had difficulty compensating the
analyte value obtained from substantially continuous output signals
terminating in an end-point reading, which is correlated with the
analyte concentration of the sample.
For many continuous processes, such as a Cottrell decay recorded
from a relatively long duration potential input signal, the decay
characteristics of the output signal may be described from existing
theory with a decay constant. However, this constant may be less
sensitive or insensitive to the physical characteristics of the
sample or the operation conditions of the system.
One method of implementing error compensation is to use a gated
input signal as opposed to substantially continuous input signal.
In these gated or pulsed systems, the changes in the input signal
perturbate the reaction of the sample so that compensation
information may be obtained. However, for analysis systems using
substantially continuous input signals to drive the reaction
(commonly electrochemical coulometry or Cottrell-decay amperometry)
and for analysis systems that observe a reaction that is started
and observed until an end-point is reached (commonly optical), the
compensation information as obtained from a perturbation of the
reaction of the sample is unavailable. Even in a sample perturbated
by a gated input signal, additional compensation information may be
available during the continuous portions of the input signal, which
may not otherwise be used by conventional error compensation
techniques.
Accordingly, there is an ongoing need for improved biosensor
systems, especially those that may provide increasingly accurate
determination of sample analyte concentrations when an end-point
reading from a substantially continuous output signal is correlated
with the analyte concentration of the sample and/or when
compensation information is unavailable from a perturbation of the
reaction. The systems, devices, and methods of the present
invention overcome at least one of the disadvantages associated
with conventional biosensor systems.
SUMMARY
In one aspect, the invention provides a method for determining an
analyte concentration in a sample that includes applying an input
signal to a sample including an analyte; generating an output
signal responsive to a concentration of the analyte in the sample
and an input signal; determining a compensated value from the
output signal in response to a conversion function and a segmented
signal processing function; and determining the analyte
concentration in the sample with the compensated value. A
conversion function may be used to convert the output signal to an
uncompensated value prior to compensating the value. The
uncompensated value may be an uncompensated analyte concentration
value.
In another aspect of the invention, there is a method of
determining an analyte concentration in a sample that includes
generating an output signal responsive to a concentration of an
analyte in a sample and an input signal, determining a compensated
value from the output signal in response to a conversion function,
a primary function, and a segmented signal processing function, and
determining the analyte concentration in the sample from the
compensated value.
In another aspect of the invention, there is a method of
determining an analyte concentration in a sample that includes
generating an output signal responsive to a concentration of an
analyte in a sample and an input signal, determining a compensated
value from the output signal in response to a conversion function,
a primary function, a first residual function, and a segmented
signal processing function, and determining the analyte
concentration in the sample from the compensated value. The primary
function may include an index function or a complex index function
and preferably corrects the error arising from hematocrit levels
and temperature or from temperature and total hemoglobin levels in
blood samples.
In another aspect of the invention, there is a biosensor system for
determining an analyte concentration in a sample that includes a
test sensor having a sample interface in electrical or optical
communication with a reservoir formed by the sensor and a
measurement device having a processor connected to a sensor
interface through a signal generator, the sensor interface having
electrical or optical communication with the sample interface, and
the processor having electrical communication with a storage
medium. The processor instructs the signal generator to apply an
electrical input signal to the sensor interface, determines an
output signal value responsive to the concentration of the analyte
in the sample from the sensor interface, and compensates at least
50% of the total error in the output signal value with a primary
function. Where if the primary function is not an segmented signal
processing function, the processor compensates at least 5% of the
remaining error in the output signal with a segmented signal
processing function, the segmented signal processing function
previously stored in the storage medium, to determine a compensated
value, and determines the analyte concentration in the sample from
the compensated value. The measurement device of the biosensor
system is preferably portable.
In another aspect of the invention, there is a method of
determining a segmented signal processing function that includes
selecting multiple segmented signal processing parameters as
potential terms in the segmented signal processing function,
determining a first exclusion value for the potential terms,
applying an exclusion test responsive to the first exclusion value
for the potential terms to identify one or more of the potential
terms for exclusion from the segmented signal processing function,
and excluding one or more identified potential terms from the
segmented signal processing function.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention can be better understood with reference to the
following drawings and description. The components in the figures
are not necessarily to scale, emphasis instead being placed upon
illustrating the principles of the invention.
FIG. 1A represents a method for determining an analyte
concentration in a sample of a biological fluid using Segmented
Signal Processing (SSP).
FIG. 1B represents a method of segmenting an output signal.
FIG. 1B-1 represents a continuous output signal ending in an
end-point reading from which the analyte concentration in a sample
may be determined.
FIG. 1B-2 represents a gated output signal including the currents
measured from three input excitations separated by two
relaxations.
FIG. 1C represents a method of processing output signal
segments.
FIG. 1D represents a method for selecting terms for inclusion in a
complex index function which may serve as an SSP function.
FIG. 2A represents a method of error compensation including a
conversion function incorporating primary compensation and SSP
parameter compensation.
FIG. 2B represents a method of error compensation including a
conversion function and SSP parameter compensation.
FIG. 2C represents a method of error compensation including a
conversion function, primary compensation, first residual
compensation, and second residual compensation provided by SSP
parameter compensation.
FIG. 3A and FIG. 3B depict the output signals in the form of
reflectance as a function of time from an optical laminar flow
system where two channels of chemical reaction and optical
detection perform the same analysis to increase accuracy.
FIG. 3C shows the correlation plot relating residual error after
conversion and primary compensation to the ability of the SSP
function to describe the residual error in relation to the
reference %-A1c concentration of the samples for channel 1.
FIG. 3D shows the correlation plot relating residual error after
conversion and primary compensation to the ability of the SSP
function to describe the residual error in relation to the
reference %-A1c concentration of the samples for channel 3.
FIG. 3E and FIG. 3F compare the results from the analysis with
using a conversion and an internalized algebraic primary
compensation with the compensated analyte concentration after use
of the SSP function in addition to the internalized algebraic
primary compensation.
FIG. 4A depicts the output signals from an electrochemical
amperometric analysis when two relatively long excitations
separated by a relatively long relaxation are applied to a sample
of blood containing glucose.
FIG. 4B shows the dose response lines when this analysis was
performed on multiple blood samples at approximately 25.degree. C.,
but with hematocrit contents of 20%, 40%, and 60% and glucose
concentrations from 0 to 700 mg/dL.
FIG. 4C plots the differentials of each output signal segment
normalized by the end-point value of the second excitation.
FIG. 4D plots the differentials of each output signal segment
normalized by the end-point value of the excitation from which the
segment values were recorded.
FIG. 4E plots the time-based differentials of each output signal
segment normalized by the end-point value of the excitation from
which the segment values were recorded.
FIG. 4F compares the total relative error (.DELTA.G/G) of the
uncompensated and SSP function compensated analyte concentrations
determined from multiple blood samples including from 20% to 60%
(volume/volume) hematocrit and glucose concentrations from
approximately 50 to 700 mg/dL at approximately 25.degree. C.
FIG. 5A depicts the input signals applied to the test sensor for an
electrochemical gated amperometric analysis where six relatively
short excitations are separated by five relaxations of varying
duration.
FIG. 5B depicts the output current values recorded from the six
excitations and the secondary output signal.
FIG. 6A is a correlation plot comparing the total error to the
predicted error of the analyte concentrations determined using only
the primary function.
FIG. 6B is a correlation plot comparing the total error to the
predicted error of the analyte concentrations determined using the
primary and first residual function.
FIG. 6C is a correlation plot comparing the total error to the
predicted error of the analyte concentrations determined using the
primary function, first residual function, and SSP function.
FIG. 6D and FIG. 6E compare the compensation results from
primary+first residual and additional compensation with the SSP
function.
FIG. 7A represents the input signals applied to the working and
counter electrodes of a test sensor for an electrochemical combined
gated amperometric and gated voltammetric analysis.
FIG. 7B shows the currents obtained for multiple analyses from the
third voltammetric excitation of a seven excitation input signal
having two amperometric and five voltammetric excitations.
FIG. 7C shows the currents obtained from the third voltammetric
excitation when the blood samples included about 400 mg/dL
glucose.
FIG. 7D represents how the output currents from the third
voltammetric excitation were segmented to provide three output
signal segments from the excitation.
FIG. 7E shows the currents measured at 5.2 seconds from the third
gated voltammetric excitation for blood samples including about 80
mg/dL, 170 mg/dL, 275 mg/dL, or 450 mg/dL glucose with hematocrit
levels of 25%, 40%, or 55% by volume.
FIG. 7F shows the glucose readings obtained from the measurement
device with and without compensation provided by the SSP
function.
FIG. 7G compares the relative error between the determined SSP
compensated and uncompensated glucose analyte concentrations for
the blood samples.
FIG. 8 depicts a schematic representation of a biosensor system
that determines an analyte concentration in a sample of a
biological fluid.
DETAILED DESCRIPTION
Analysis error and the resultant bias in analyte concentrations
determined from the end-point of a previously continuous output
signal may be reduced by segmented signal processing (SSP) of the
previously continuous output signal. By dividing the continuous
output signal into segments, and converting one or more of the
segments into an SSP parameter, an SSP function may be determined.
The SSP function may be used singularly or in combination with
other functions to reduce the total error in the analysis. The
error from the biosensor system may have multiple error sources or
contributors arising from different processes/behaviors that are
partially or wholly independent.
As SSP compensation arises from the segmenting of an otherwise
continuous output signal, the analysis error may be compensated in
biosensor systems where compensation based on the output signals
from the analyte or analyte responsive measurable species were
previously unavailable. Additionally, even in perturbated systems,
such as those based on gated amperometry or voltammetry, SSP
compensation can implement compensation not dependent on the
perturbations arising from the gated input signal.
Residual error compensation may substantially compensate for the
total error in an analysis until the error becomes random. Random
error is that not attributable to any error contributor and not
described by a primary or residual function at a level considered
to be statistically significant. An SSP function may provide the
primary compensation or the residual compensation to the error
correction system. Alternatively the SSP function may be used with
a first residual function to provide second residual function
compensation to the error correction system. In each of these
instances, the SSP function focuses on correcting different error
parameters than are compensated by the other compensations.
FIG. 1A represents a method for determining an analyte
concentration in a sample of a biological fluid using Segmented
Signal Processing (SSP). In 110, the biosensor system generates an
output signal responsive to an analyte concentration in a sample of
a biological fluid in response to a light-identifiable species or
an oxidation/reduction (redox) reaction of the analyte. In 120, the
biosensor system measures the output signal responsive to the
analyte concentration from the sample. In 130, the biosensor system
segments at least a portion of the output signal. In 140, the
biosensor system processes one or more of the output signal
segments to generate at least one SSP parameter. In 150, the
biosensor system determines the analyte concentration from a
compensation method including at least one SSP parameter and the
output signal. In 160, the compensated analyte concentration may be
displayed, stored for future reference, and/or used for additional
calculations.
In 110 of FIG. 1A, the biosensor system generates an output signal
in response to a light-identifiable species or an
oxidation/reduction (redox) reaction of an analyte in a sample of a
biological fluid. The output signal may be generated using an
optical sensor system, an electrochemical sensor system, or the
like.
In 120 of FIG. 1A, the biosensor system measures the output signal
generated by the analyte in response to the input signal applied to
the sample, such as from a redox reaction of the analyte. The
system may measure the output signal continuously or intermittently
from continuous or gated excitations. For example, the system may
continuously measure the electrical signal from an optical detector
responsive to the presence or concentration of an optically active
species until an end-point reading is obtained. Similarly, the
system may continuously measure the electrical signal from an
electrode responsive to the presence or concentration of a redox
species until an end-point reading is obtained.
The biosensor system also may measure the output signal
continuously or intermittently during the excitations of a gated
amperometric or voltammetric input signal, resulting in multiple
current values being recorded during each excitation. In this
manner, an end-point reading may be obtained at the end of one or
more of the multiple input excitations. The biosensor may measure
the output signal from the analyte directly or indirectly through
an electrochemical mediator. In an optical system, the detector may
measure light directly from the analyte or from an optically active
species responsive to the concentration of the analyte in the
sample to provide the output signal.
An end-point reading is the last operative data point measured for
an output signal that has been ongoing. By "last operative" it is
meant that while the actual last data point, the second to the last
data point, or the third to the last data point, for example, may
be used, the end-point reading is the data point reflecting the
last state of the analysis for the preceding input signal.
Preferably, the end-point reading will be the last data point
measured from a specific excitation of the input signal for an
electrochemical system. Preferably, the end-point reading will be
the last data point measured from the input signal for an optical
or other continuous input system.
In 130 of FIG. 1A, the biosensor system segments at least a portion
of the output signal. The measurement device of the biosensor
system segments at least a portion of the output signal in response
to a previously determined segmenting routine. Thus, the output
signal values to be measured and represent a particular segment for
SSP parameter determination are previously determined before the
analysis. Segmenting of the output signal is further discussed
below with regard to FIG. 1B.
In 140 of FIG. 1A, the biosensor system processes the output signal
values with an SSP parameter processing method to generate at least
one SSP parameter. Preferably, at least one SSP parameter is
generated from each segment. Generating SSP parameters from the
segments of the output signal is further discussed below with
regard to FIG. 1C. Unlike compensation systems using one end-point
reading to compensate another end-point reading, the SSP parameters
originate from values determined before an end-point reading is
obtained or before and after an intermediate end-point reading is
obtained.
In 150 of FIG. 1A, the biosensor system determines the analyte
concentration of the sample from a method of error compensation
including at least one SSP parameter and the output signal. The
method of error compensation may be slope-based or another method.
The at least one SSP parameter may be incorporated into a method of
error compensation relying on a conversion function, a method of
error compensation relying on a conversion function internalizing a
primary compensation, a method of error compensation relying on a
distinct conversion function and a distinct primary compensation,
and any of these methods of error compensation also including first
and/or second residual function compensation. Preferably, a complex
index function generated from multiple SSP parameters is used in
combination with an output signal value to determine the analyte
concentration of the sample. While the SSP parameter is preferably
used to compensate during or after the output signal has been
converted to an analyte concentration by the conversion function,
the SSP parameter could be applied to the output signal before the
signal is converted to an analyte concentration.
The SSP function can compensate at least three types of error in
the output signal measured from the test sensor. The SSP function
may be used to directly compensate the total error present in the
output signal when a conversion function is used to convert the
output signal into a sample analyte concentration in response to a
reference correlation lacking compensation for any error
contributors. The SSP function also may be used to compensate when
conversion and primary compensation is used to reduce the error
attributable to the major error contributors, such as temperature,
hematocrit, and hemoglobin. The SSP function also may be used to
compensate when conversion, primary compensation, and first
residual compensation are used, thus when primary compensation has
reduced major error and residual compensation has reduced
additional error, such as the user self-testing error. Thus, the
SSP function may be considered to compensate relative error in
analyte concentrations determined from the sample with conversion
and SSP compensation, with conversion, primary compensation, and
SSP compensation, or with conversion, primary compensation,
residual compensation, and SSP compensation.
FIG. 1B represents a method of segmenting an output signal for use
in accord with 130 of FIG. 1A. In 132, the output signal is related
to time. While time is preferred, another consistently changing
metric could be used. In 134, a regular or irregular segmenting
interval with respect to time or the other consistently changing
metric is chosen. The type of interval selected to segment the
output signal is preferably selected based on the portions of the
output signal showing the greatest absolute change at a selected
time. In 136, the values of the output signal are segmented into
individual segments in response to the regular or irregular
segmenting interval. Preferably, the output signal is segmented
into at least three segments, more preferably at least four. Once
the desired segments are determined for the biosensor system, they
may be implemented as the segmenting routine in the measurement
device. In this manner the measurement device selects which output
signal values to assign to which segment for SSP parameter
determination.
FIG. 1B-1 represents a continuous output signal ending in an
end-point reading from which the analyte concentration in a sample
may be determined. In this illustration, the output signal was
segmented into output signal segments (a) through (k). Thus,
segment (a) is from the time period when the output signal started
and segment (k) is from the time period where the end-point reading
was made before the analysis was terminated. The end-point reading
may be correlated with the analyte concentration of the sample
though a linear or non-linear relationship. The output signals may
be segmented at regular or irregular intervals with respect to
time.
FIG. 1B-2 represents the output signal from a gated amperometric
input signal including the currents measured from three input
excitations separated by two relaxations. Each excitation ends in
an end-point reading from which the analyte concentration or
another value relevant to the analysis may be determined. In this
illustration, each of the three output signals was segmented into
output signal segments (a) through (d). Thus, segment 1a is from
the time period when the output signal from the first excitation
started and segment 1d is from the time period where the end-point
reading for the first excitation was recorded before the first
relaxation period. The end-point reading may be correlated with the
analyte concentration of the sample or other values relevant to the
analysis, such as error parameters, though a linear or non-linear
relationship. The output signals may be segmented at regular or
irregular intervals with respect to time.
FIG. 1C represents a method of processing output signal segments to
provide SSP parameters in accord with 140 of FIG. 1A. In 142, the
correlation between one or more SSP parameters and an error
contributor of the analysis was previously determined. The
correlation may be determined in the laboratory between a potential
SSP parameter and error arising from primary error sources, such as
hematocrit, temperature, and total hemoglobin in blood samples, or
from residual error sources remaining after primary compensation.
In 144, segmented signal processing is applied to the output signal
values corresponding to one or more predetermined segments.
Preferably, the output signal values from at least two segments are
processed. More preferably, the output signal values from at least
three segments are processed. In 146, an SSP parameter is generated
from the output signal values corresponding to the one or more
predetermined segments. Preferably, at least two SSP parameter
values are generated, more preferably at least three SSP parameters
are generated from the one or more predetermined segments.
Any method that converts multiple output values into a single
parameter may be used to determine the SSP parameters, however,
preferable SSP parameter determining methods include averaging of
signals within a segment, determining ratios of the signal values
from within a segment, determining differentials of the signal
values from within a segment, determining time base differentials,
determining normalized differentials, determining time-based
normalized differentials, determining one or more decay constants
and determining one or more decay rates. For example, the
normalized differential method may be implemented by obtaining the
differential between the first and the last data point (e.g.
current value) for each segment, followed by normalization with the
end-point reading of the output signal, or by an intermediate
end-point reading of the respective segment or from another
segment, for example. Thus, the normalized differential method may
be expressed as: (a change in current/the corresponding change in
time)/the end-point selected for normalization. General equations
representing of each of these SSP parameter determining methods are
as follows:
Averaging of signal values from within a segment:
(Avg)=(i.sub.n+i.sub.m)/2, where i.sub.n is a first output signal
value and i.sub.m is a second output signal value of the segment
and where i.sub.n is preferably greater than i.sub.m;
Determining ratios of the signal values from within a segment:
(Ratio)=i.sub.m/i.sub.n;
Determining differentials of the signal values from within a
segment: (Diff)=i.sub.n-i.sub.m,
Determining time-based differentials: Time-based differential
(TD)=(i.sub.n-i.sub.m)/(t.sub.m-t.sub.n), where t.sub.m is the time
at which the i.sub.m output signal value was measured and t.sub.n
is the time at which the i.sub.n output signal value was
measured;
Determining normalized differentials: Normalized differential (Nml
Diff)=(i.sub.n-i.sub.m)/i.sub.end, where i.sub.end is the end-point
output signal value of the segment or as described further
below;
Determining time-based normalized differentials: Time-based
normalized differential
(TnD)=(i.sub.n-i.sub.m)/(t.sub.m-t.sub.n)/i.sub.end;
Determining one or more decay constants: Decay constant
(K)=[ln(i.sub.n)-ln(i.sub.m)]/[ln(t.sub.m)-ln(t.sub.n)]=.DELTA.
ln(i)/[-.DELTA. ln(t)], for a general function relating output
signal current values that decay as a function of time to analyte
concentration by i=A*t.sup.K, where ln represents a logarithmic
mathematical operator, "A" represents a constant including analyte
concentration information, "t" represents time, and "K" represents
the decay constant; and
Determining one or more decay rates: Decay rate
(R)=[ln(i.sub.m)-ln(i.sub.n)]/(1/t.sub.m-1/t.sub.n), for an
exponential function of i=A*exp(R/t), where "exp" represents the
operator of the exponential function, and "R" represents the decay
rate.
The end-point reading preferably used for normalization is that
which is the last current recorded for the excitation being
segmented, the last current recorded for the analysis, or the
current that correlates best with the underlying analyte
concentration of the sample. Other values may be chosen for the
normalization value. Normalization preferably serves to reduce the
influence of different sample analyte concentrations on the
determined SSP parameters.
FIG. 1D represents a method for selecting terms for inclusion in a
complex index function which may serve as an SSP function. In 152,
multiple SSP parameters are selected as terms for potential
inclusion in the complex index function. In addition to the SSP
parameters, one or more error or other parameters also may be
included in the function. As with the SSP parameters, error
parameters may be obtained from an output signal responsive to a
light-identifiable species or from the redox reaction of an analyte
in a sample of a biological fluid. The error parameters also may be
obtained independently from the output signal, such as from a
thermocouple. The terms of the complex index function may include
values other than SSP and error parameters, including values
representing the uncompensated concentration of the analyte in the
sample and the like. In 154, one or more mathematical techniques
are used to determine first exclusion values for each selected
term. The mathematical techniques may include regression,
multi-variant regression, and the like. The exclusion values may be
p-values or the like. The mathematical techniques also may provide
weighing coefficients, constants, and other values relating to the
selected terms.
In 156, one or more exclusion tests are applied to the exclusion
values to identify one or more terms to exclude from the complex
index function. At least one term is excluded under the test.
Preferably, the one or more exclusion tests are used to remove
statistically insignificant terms from the complex index function
until the desired terms are obtained for the function. In 157, the
one or more mathematical techniques are repeated to identify second
exclusion values for the remaining terms. In 158, if the second
exclusion values do not identify remaining terms for exclusion from
the complex index function under the one or more exclusion tests,
the remaining terms are included in the complex index function. In
159, if the second exclusion values identify remaining terms to
exclude from the complex index function under the one or more
exclusion tests, the one or more mathematical techniques of 157 may
be repeated to identify third exclusion values for the remaining
terms. These remaining terms may be included in the complex index
function as in 158 or the process may be iteratively repeated as in
159 until the exclusion test fails to identify one or more terms to
exclude. Additional information regarding the use of exclusion
tests to determine the terms and weighing coefficients for complex
index functions may be found in U.S. application Ser. No.
13/053,722, filed Mar. 22, 2011, entitled "Residual Compensation
Including Underfill Error".
FIG. 2A represents a method of error compensation including a
conversion function incorporating primary compensation 210 and SSP
parameter compensation. The output from the conversion function
incorporating primary compensation 210 and including residual error
225 is compensated with SSP parameters in the form of an SSP
function 250. Thus, the SSP function 250 compensates the
uncompensated output values 205 after conversion and primary
compensation. The total error 215 includes all error in the
analysis, such as random and/or other types of error. The
conversion function 210 and the SSP function 250 may be implemented
as two separate mathematical equations, a single mathematical
equation, or otherwise. For example, the conversion function 210
may be implemented as a first mathematical equation and the SSP
function 250 implemented as a second mathematical equation.
In FIG. 2A, uncompensated output values 205 may be output currents
responsive to an optical or electrical input signal generating an
output signal having a current component. The uncompensated output
values may be output signals having a current or potential
component responsive to the light detected by one or more detectors
of an optical system. The uncompensated output values may be output
potentials responsive to potentiometry, galvanometry, or other
input signals generating an output signal having a potential
component. The output signal is responsive to a measurable species
in the sample. The measurable species may be the analyte of
interest, a species related to the analyte, an electrochemical
mediator whose concentration in the sample is responsive to that of
the analyte of interest, or a light-identifiable species whose
concentration in the sample is responsive to that of the analyte of
interest.
The conversion function 210 is preferably from a predetermined
reference correlation between the uncompensated output values 205
generated from a sample in response to an input signal from a
measurement device and one or more reference analyte concentrations
previously determined for known physical characteristics and
environmental aspects of the sample. For example, the conversion
function 210 may be able to determine the glucose concentration in
a blood sample from the output values 205 based on the sample
having a hematocrit content of 42% when the analysis is performed
at a constant temperature of 25.degree. C. In another example, the
conversion function 210 may be to determine the %-A1c in a blood
sample from the output values 205 based on the sample having a
specific total hemoglobin content when the analysis is performed at
a constant temperature of 23.degree. C. The reference correlation
between known sample analyte concentrations and uncompensated
output signal values may be represented graphically,
mathematically, a combination thereof, or the like. Reference
correlations may be represented by a program number (PNA) table,
another look-up table, or the like that is predetermined and stored
in the measurement device of the biosensor system.
The primary compensation incorporated into the conversion function
210 substantially compensates the major error contributor/s
introducing error into the uncompensated output values 205. Thus,
in an optical biosensor system that determines the %-A1c in blood,
the major error contributors are temperature and total hemoglobin.
Similarly, in an electrochemical biosensor system that determines
the glucose concentration in blood, the major error contributors
are temperature and hematocrit.
The primary function providing the primary compensation may be
algebraic in nature, thus linear or non-linear algebraic equations
may be used to express the relationship between the uncompensated
output values and the error contributors. For example, in a %-A1c
biosensor system, temperature (T) and total hemoglobin (THb) are
the major error contributors. Similarly to hematocrit error in
blood glucose analysis, different total hemoglobin contents of
blood samples can result in different A1c signals erroneously
leading to different A1c concentrations being determined for the
same underlying A1c concentration. Thus, an algebraic equation to
compensate these error may be
A1c=a.sub.1*S.sub.A1c+a.sub.2/S.sub.A1c+a.sub.3*THb+a.sub.4*THb.sup.2,
where A1c is the analyte concentration after conversion of the
uncompensated output values and primary compensation for total
hemoglobin, S.sub.A1c is the temperature compensated output values
(e.g. reflectance or adsorption) representing A1c, and THb is the
total hemoglobin value calculated by
THb=d.sub.0+d.sub.1/S.sub.THb+d.sub.2/S.sub.THb.sup.2+d.sub.3/S.sub.THb.s-
up.3, where S.sub.THb is the temperature corrected THb reflectance
signal obtained from the test sensor. The temperature effects for
S.sub.A1c and S.sub.THb are corrected with the algebraic
relationship
S.sub.A1c=S.sub.A1c(T)+[b.sub.0+b.sub.1*(T-T.sub.ref)+b.sub.2*(T-T.sub.re-
f).sup.2] and S.sub.THb=[S.sub.THb (T)
c.sub.0+c.sub.1*(T-T.sub.ref)]/[c.sub.2*(T-T.sub.ref).sup.2]. By
algebraic substitution, the primary compensated analyte
concentration A may be calculated with conversion of the
uncompensated output values and primary compensation for the major
error contributors of temperature and total hemoglobin being
integrated into a single algebraic equation.
The primary function also may include a slope-based function, a
complex index function, or other compensation function focusing on
the reduction of major error, such as temperature and hematocrit or
temperature and total hemoglobin, in the analysis. For a
slope-based glucose analyte example, the observed total error of a
biosensor system including a measurement device and a test sensor
may be expressed in terms of .DELTA.S/S (normalized slope
deviation) or .DELTA.G/G (relative glucose error). Suitable
slope-based primary compensation techniques may be found in Intl.
Pub. No. WO 2009/108239, filed Dec. 6, 2008, entitled "Slope-Based
Compensation" and in Intl. Pub. No. WO 2010/077660, filed Dec. 8,
2009, entitled "Complex Index Functions", for example.
Preferable primary functions that implement slope-based
compensation are index functions that may be determined using error
parameter values from the analysis of the analyte, such as the
intermediate signals from the analyte responsive output signal, or
from sources independent of the analyte responsive output signal,
such as thermocouples, additional electrodes, and the like. Error
parameters may be any value responsive to one or more error in the
output signal. Thus, the error parameters may be extracted directly
or indirectly from the output signal of the analysis and/or
obtained independently from the analytic output signal. Other error
parameters may be determined from these or other analytic or
secondary output signals. Any error parameter may be used to form
the term or terms that make up the index function, such as those
described in Intl. Pub. No. WO 2009/108239, filed Dec. 6, 2008,
entitled "Slope-Based Compensation," and the like.
An index function is responsive to at least one error parameter. An
index function may generate a calculated number that correlates
total analysis error to an error parameter, such as hematocrit or
temperature, and represents the influence of this error parameter
on bias. Index functions may be experimentally determined as a
regression or other equation relating the deviation of determined
analyte concentrations from a reference slope to the error
parameter. Thus, the index function represents the influence of the
error parameter on the slope deviation, normalized slope deviation,
or percent bias arising from the total error in the analysis.
Index functions are complex when they include combinations of terms
modified by term weighing coefficients. A complex index function
has at least two terms, each modified by a term weighing
coefficient. The combination preferably is a linear combination,
but other combination methods may be used that provide weighing
coefficients for the terms. For example, a complex index function
may have a linear combination of terms with weighing coefficients
as follows:
f(ComplexIndex)=a1+(a2)(R3/2)+(a3)(R4/3)+(a4)(R5/4)+(a5)(R3/2)(G)+(a6)(R4-
/3)(G)+(a7)(R3/2)(Temp)+(a8)(R4/3)(Temp)+(a9)(Temp)+(a10)(G)+ . . .
, where a1 is a constant and not a weighing coefficient, a2-a10
independently are term weighing coefficients, G is the determined
analyte concentration of the sample without compensation, and Temp
is temperature. Each of the term weighing coefficients (a2-a10) is
followed by its associated term--(R3/2), (R4/3), (R5/4), (R3/2)(G),
(R4/3)(G), (R3/2)(Temp), (R4/3)(Temp), (Temp), and (G). Other
complex index functions may be used including nonlinear and other
combinations of terms with weighing coefficients.
Term weighing coefficients apportion the contribution of each term
to the function. Thus, they allow for each term to have a different
apportionment to the function. Two or more of the term weighing
coefficients may be the same or similarly apportion the
contribution of their respective terms to the function. However, at
least two weighing coefficients are different or differently
apportion the contribution of their respective terms to the
function. In this way, the term weighing coefficients may be
selected to allow for the effect of one term on another term in
relation to the overall function, thus reducing or eliminating
error from the interactions of the terms when the complex index
function is used. The term weighing coefficients may have any
value, preferably numerical values other than one or zero, as a
weighing coefficient of 1 may not apportion the contribution of the
term and a weighing coefficient of 0 would result in the exclusion
of the term. The term weighing coefficients are not a single value
or constant that may be applied by algebraic disposition to all the
terms. Term weighing coefficients may be determined through the
statistical processing of the data collected from a combination of
multiple analyte concentrations, different hematocrit levels,
different total hemoglobin levels, different temperatures, and the
like.
Additionally, a complex index function is not only a "complex
function" in a mathematical sense, thus requiring or implying the
use of an imaginary number (a number with the square root of
negative one). A complex index function may include one or more
imaginary numbers, such as one of the terms or weighing
coefficients, but is not limited or restricted to having any
imaginary numbers.
Each term in a complex index function may include one or more error
parameters. The terms may be selected with one or more exclusion
tests. More preferably, primary functions are complex index
functions, such as those described in Intl. Pub. No. WO
2010/077660, filed Dec. 8, 2009, entitled "Complex Index
Functions". Other primary compensation techniques may be used.
The residual error 225 may be expressed generally by Residual
Error=total error observed-primary function corrected error. The
residual error 225 remaining in the analyte concentration not
compensated by the primary function may be considered to arise from
operating condition, manufacturing variation, and/or random error.
Of the total error in the uncompensated output values 205, primary
compensation removes at least 40% of this error from the
compensated analyte concentration 225, preferably at least 50%.
Preferably, primary compensation removes from 40% to 75% of the
total error in the uncompensated output values, and more preferably
from 50% to 85%.
FIG. 2B represents a method of error compensation including a
conversion function 210 and SSP parameter compensation. The output
from the conversion function 210 including total error 215 is
compensated with SSP parameters in the form of a SSP function 250
to provide primary compensation. Thus, the SSP function 250
compensates the uncompensated output values 205 after conversion.
The total error 215 includes primary and residual error. The total
error 215 also may include random and/or other types of error. The
conversion function 210 and the SSP function 250 may be implemented
as two separate mathematical equations, a single mathematical
equation, or otherwise. For example, the conversion function 210
may be implemented as a first mathematical equation, and the SSP
function 250 implemented as a second mathematical equation.
In FIG. 2B, the conversion function 210 and the uncompensated
output values 205 may be considered similar to those discussed with
regard to FIG. 2A, except that the conversion function 210 does not
internalize primary compensation. When the sample is blood and the
analyte is glucose, the compensation provided by the SSP function
250 may be substantially limited to compensation for analysis error
arising from temperature and/or hematocrit. Thus, by characterizing
the biosensor system with respect to temperature and/or hematocrit
change, the effects from temperature and/or hematocrit may be
compensated by the SSP function 250.
FIG. 2C represents a method of error compensation including a
conversion function 210, primary compensation, first residual
compensation, and second residual compensation provided by SSP
function compensation. The output from the conversion function 210
including total error 215 is compensated with a primary
compensation in the form of a primary function 220. The remaining
residual error 225 is compensated with a residual compensation in
the form of a first residual function 230 responsive to user
self-testing error. The remaining residual error 235 is compensated
with SSP parameters in the form of a SSP function 250. Thus, the
SSP function 250 compensates the uncompensated output values 205
after conversion, primary compensation, and first residual
compensation. The total error 215 includes primary and residual
error. The total error 215 also may include random and/or other
types of error. The conversion function 210, the primary function
220, the first residual function 230, and the SSP function 250,
which serves as a second residual function in this example, may be
implemented as four separate mathematical equations, a single
mathematical equation, or otherwise. For example, the conversion
function 210 may be implemented as a first mathematical equation,
while the primary function 220, the first residual function 230,
and the SSP function 250 are combined and implemented as a second
mathematical equation.
In FIG. 2C, the conversion function 210 and the uncompensated
output values 205 may be considered similar to those discussed with
regard to FIG. 2A. The primary function 220 may be considered a
complex index function implementing a slope-based compensation, as
previously discussed. The first residual function 230 providing at
least a portion of the residual compensation is applied in addition
to compensating the major error with the primary function 220.
The observed residual error substantially lacked the error removed
from the total error by the values of the primary function 220. The
total error includes error from substantially different sources
and/or test cases, such as temperature and hematocrit error
determined in a controlled environment (substantially described by
the primary function), versus operating condition error originating
from outside of a controlled environment (substantially described
by the residual function) and manufacturing variation. By focusing
on the residual error in a particular situation, such as user
self-testing by inexperienced subjects, and finding at least one
residual function associated with the residual error, the
measurement performance of the biosensor system may be improved.
Residual error remaining after application of the first residual
function 230 may be further reduced with the application of a
second residual function in the form of a SSP function 250.
In this example, while the error described by the SSP function may
be from either a controlled environment or a non-controlled
environment, the error is preferably non-random error from a
non-controlled environment remaining after use of a conversion
function including primary compensation, a conversion function plus
primary compensation, and/or error remaining after use of a
conversion function plus primary and first residual function
compensation. The second residual function may be selected to
compensate systematic deficiencies in the compensation provided by
the primary or primary and first residual functions. Preferably,
the error corrected by the SSP function shows a lower correlation
with the primary and/or first residual functions than with the SSP
function.
In addition to including primary compensation, first residual
compensation, and at least one SSP compensation, the method of
error compensation represented in FIG. 2C may include the ability
to adjust the compensation provided by the primary compensation in
relation to the compensation provided by the residual compensation
in relation to the compensation provided by the SSP compensation.
The residual compensation also may include the ability to adjust
the compensation provided by the first residual function in
relation to the compensation provided by the SSP function.
The error compensation provided by the primary compensation in
relation to the compensation provided by the residual and SSP
compensations may be adjusted because the function or functions
making up the first residual compensation may be taken from
predetermined values stored in the measurement device as a database
or otherwise for a limited temperature and/or hematocrit range,
while the primary and SSP functions may be determined from a full
range of sample temperature and hematocrit content. Thus, the
primary and SSP functions may be determined from inputs acquired
during the analysis of a sample, while a finite number of first
residual functions may be predetermined and stored in the
measurement device. The error compensation provided by the primary
and SSP compensations in relation to the compensation provided by
the first residual compensation also may be adjusted because some
overlap may occur between the error described by the primary, the
SSP, and one or more residual functions. There may be other reasons
to adjust the error compensation provided by the primary and SSP
compensations in relation to the compensation provided by the
residual compensation.
One method of adjusting the error compensation provided by the
primary and SSP compensations in relation to the compensation
provided by the first residual compensation includes the use of
function weighing coefficients. Compensation in a general form,
where the error compensation provided by the primary and SSP
compensations is adjusted in relation to the compensation provided
by the residual compensation, may be expressed as: Primary
function+WC1*Residual function+WC2*SSP function, where WC1 and WC2
are the function weighing coefficients for the two compensation
types. The function weighing coefficient WC may be selected as a
function of temperature and/or hematocrit for varying compensation
contributions from the first residual function and the SSP
function. Similarly, compensation including one or more residual
functions and an SSP function where the residual functions are each
modified by a function weighing coefficient may take the following
general forms: Compensated analyte concentration=current
nA/(Slope.sub.Cal*(1+primary function+WC1*residual1+WC2*residual2 .
. . +WC3*SSP function)),
or using the alternative general form of residual: Compensated
analyte concentration=current nA/(Slope.sub.Cal*(1+primary
function)*(1+WC1*residual1)*(1+WC2*residual2) . . . *(1+WC3*SSP
function), where WC1, WC2, and WC3 are function weighing
coefficients having values between 0 and 1 and allow the effect of
the residual function/s and SSP function to be reduced when
conditions are outside those that were used to develop the residual
function. While similar in operation to the term weighing
coefficients previously discussed, function weighing coefficients
apportion the contribution of each compensation function to the
total compensation in response to the total error.
Residual1 is the first level of residual compensation after the
primary compensation function, while Residual2 is the next level of
residual compensation, but may not be available if an error
source/index function is not found. Residual1 and Residual2 are
preferably independent of each other and of the primary function.
Preferably, the SSP function is independent of the primary and
residual functions.
Function weighing coefficients for the primary, versus first
residual compensation, versus SSP compensation may be predetermined
and stored in the measurement device in the form of a table or
through other means. For example, the WC1, WC2, and WC3 values may
be characterized in a two-dimensional table as a function of
temperature and hematocrit. In this way, the function weighing
coefficient table may be structured to improve the measurement
performance of the biosensor system by reducing the effect of the
residual function or functions on the determined analyte
concentration when the hematocrit content of the sample and the
temperature at which the analysis is performed are relatively close
to the conditions under which the data was obtained that was used
to determine the conversion function 210. Additional information
addressing residual compensation and weighing coefficients may be
found in U.S. application Ser. No. 13/053,722, filed Mar. 22, 2011,
entitled "Residual Compensation Including Underfill Error".
Biosensor systems having the ability to generate additional output
values external to those from the analyte or from the
mediator/light-identifiable species responsive to the analyte also
may benefit from the previously described methods of error
compensation. Systems of this type generally use the additional
output value or values to compensate for interferents and other
contributors by subtracting the additional output value or values
from the analyte responsive output signal in some way. Error
parameters may be extracted directly or indirectly from the output
signal of the analysis and/or obtained independently from the
output signal. Thus, the additional output values external to those
from the analyte or from the mediator responsive to the analyte may
be used to form terms, such as those described in Intl. Pub. No. WO
2009/108239, filed Dec. 6, 2008, entitled "Slope-Based
Compensation," and the like.
FIG. 3A and FIG. 3B depict the output signals in the form of
reflectance as a function of time from an optical laminar flow
system where two channels of chemical reaction and optical
detection perform the same analysis to increase accuracy. Each
detection channel detects both A1c and total hematocrit (THb)
reflectance signals. FIG. 3A shows the typical response of
reflectance profile for channels 1 and 2, and 3 and 4, respectively
from two separate strips within the laminar flow test sensor.
Channels 1 and 3 are the A1c reflectance output signals, while
channels 2 and 4 are the total hemoglobin reflectance output
signals. FIG. 3B shows a longer time base for channels 1 and 3.
Having an end-point signal for each channel, SSP was applied to the
continuous reflectance profile for each channel. The output signal
(A1c reflectance profile) was segmented into five segments, which
are designated as D1-1, D1-2, D1-3, D1-4 and D1-5 for the channel 1
A1c reading spot (CH1) and D3-1, D3-2, D3-3, D3-4 and D3-5 for the
channel 3 A1c reading spot (CH3).
The plots show two segments before the minimum reflectance (Min-R)
(D1-1 and D1-2), one immediately after Min-R (D1-3), one in the
beginning stage of approaching a steady state (D1-4), and one
representing the last stage toward the end-point signal R-100
(D1-5). The output signals were segmented and processed using a
time based differential, .DELTA.R/.DELTA.t, which is unit-less.
Other methods of segmenting and processing the output signals may
be used.
In FIG. 3A and in FIG. 3B, the x-axis is expressed in numerical
values internalizing time because of the irregular data acquisition
interval. Before and right after Min-R, the time unit is 0.3
seconds per .about.0.25. While after Min-R has past, each numerical
value represents 3 seconds, which leads to 300 seconds at the
end-point reading R-100. Thus, for the time base numbers 2 through
7 on the x-axis, each number includes 4 data points separated by
0.3 seconds (4 data points are included between 2 and 3 along the
x-axis). Similarly, for the time base numbers 7 to 42 on the
x-axis, 1 data is point, separated by 3 seconds, is included per
time base number. With regard to the actual length of the analysis,
the time base number 10 on the x-axis of FIG. 3A represents about
30 seconds having passed since the start of the analysis. In FIG.
3B, the time base number 40 on the x-axis represents approximately
120 seconds having passed since the start of the analysis, and the
time base number 40 represents the passage of approximately 300
seconds since the start of the reaction.
The output signal segments were then processed to provide SSP
parameters and their cross-terms and then considered as terms for
potential inclusion in the complex index function, which served as
the SSP function. Table 1, below, lists the weighing coefficients
selected in view of the exclusion test/s resulting from a
multi-variable regression of SSP parameters and cross-terms that
combine an SSP parameter with an additional value. MINITAB version
14 software was used with the Multi-Variant Regression of Linear
Combinations of Multiple Variables option chosen to perform the
multi-variable regression. Other statistical analysis or regression
options may be used to determine the weighing coefficients for the
terms.
TABLE-US-00001 TABLE 1 Results of optical multivariable regression
from output signal of channel 1. Weighing Terms Coefficients Temp
0.032659 MR1 1.3669 D1-1*A1 0.13053 D1-3*A1 1.3798 D1-4*A1 -3.1767
D1-5*A1 -170.02 D3-1*A3 0.24341 D3-2*A3 0.26661 D3-3*A3 -0.20696
D1-1*A3 -0.12288 D1-5*A3 114.50 D3-1*A1 -0.24499 D3-2*A1 -0.28015
A1Mt1D1-3 -0.48557 A1Mt1D1-5 29.822 Mt1*D1-3 1.4891 Mt1*D1-5
-166.94
The resulting complex index function which served as the SSP
function for channel 1 may be represented as follows: SSP Function
CH1=-0.88664+0.03266*`T`+1.367*`MR1`+0.1305*`D1-1*A1`+1.3798*`D1-3*A1`-3.-
177*`D1-4*A1`-170*`D1-5*A1`+0.2434*`D3-1*A3`+0.2666*`D3-2*A3`-0.207*`D3-3*-
A3`-0.1229*`D1-1*A3`+114.5*`D1-5*A3`-0.245*`D3-1*A1`-0.2802*`D3-2*A1`-0.48-
56*`A1Mt1D1-3`+29.82*`A1Mt1D1-5`+1.489*`Mt1*D1-3`-166.9*`Mt1*D1-5`
where -0.88664 is a constant, T is temperature, MR1 is the
reflectance at the minimum reflectance (Min-R) from channel 1, A1
is A1c concentration determined from channel 1 using the conversion
function internalizing primary compensation, A3 is the A1c value
from channel 3, D1-1 through D1-5 are the SSP parameters from
output signal segments D1-1 through D1-5 in FIG. 3A, and Mt1 is the
time at which the Min-R reflectance was recorded from channel
1.
FIG. 3C shows the correlation plot relating residual error after
conversion and primary compensation to the ability of the SSP
function to describe the residual error in relation to the
reference %-A1c concentration of the samples for channel 1. Thus,
the SSP function for channel 1 was able to describe nearly 60%
(R.sup.2=59.3) of the error remaining after the uncompensated
output values were converted and primary compensation was applied
to compensate for temperature and total hemoglobin error.
Preferably, the SSP function will describe at least 50% of the
residual error remaining after application of the conversion and
primary compensation functions to the uncompensated output values
from the test sensor.
A similar process was repeated for the output signal from channel
3. The results are presented in Table 2, below.
TABLE-US-00002 TABLE 2 Results of optical multivariable regression
from output signal of channel 3. Weighing Terms Coefficients Temp
0.028506 D1-1*A1 0.18950 D1-2*A1 0.14789 D1-5*A1 -38.919 D3-3*A3
1.2120 D3-5*A3 -194.99 D1-1*A3 -0.18606 D1-2*A3 -0.14913 D1-4*A3
-4.4662 D3-2*A1 -0.038527 D3-5*A1 165.77 A3MR3D3-3 -5.757 A3MR3D3-5
501.29 A3MRt3D3-5 -8.354 Mt3*D3-2 0.031573 Mt3*D3-4 3.4435
The resulting complex index function which served as the SSP
function for channel 3 may be represented as follows: SSP Function
CH3=-0.68117+0.02851*`T`+0.1895*`D1-1*A1`+0.14789*`D1-2*A1`-38.919*`D1-5*-
A1`+1.212*`D3-3*A3`-195*`D3-5*A3`-0.18606*`D1-1*A3`-0.14913*`D1-2A3`-4.466-
2*`D1-4A3`-0.038527*`D3-2*A1`+165.77*`D3-5*A1`-5.757*`A3MR3D3-3`+501.29*`A-
3MR3D3-5`-8.354*`A3MRt3D3-5`+0.031
573*`Mt3*D3-2`+3.4435*`Mt3*D3-4`
FIG. 3D shows the correlation plot relating residual error after
conversion and primary compensation to the ability of the SSP
function to describe the residual error in relation to the
reference %-A1c concentration of the samples for channel 3. Again,
the SSP function for channel 3 was able to describe nearly 60%
(R.sup.2=57.8) of the error remaining after the uncompensated
output values were converted and primary compensation was applied.
Both the SSP CH1 and CH3 functions were the compensation functions
representing the relative errors of channels 1 and 3
(.DELTA.A1c/A1c).sub.1, (.DELTA.A1c/A1c).sub.3. Compensation was
carried out as follows: A1c.sub.comp1=A1c.sub.raw1/(1+SSP1) and
A1c.sub.comp3=A1c.sub.raw1/(1+SSP3. The final A1c value was
determined with the general relationship
A1c.sub.final=(A1c.sub.comp1+A1c.sub.comp3)/2, and was the average
from channels 1 and 3.
FIG. 3E and FIG. 3F compare the results from the analysis using a
conversion function with an internalized algebraic primary
compensation verses using the same conversion function with
internalized primary compensation and the addition of SSP function
compensation. Five different lots of test sensors were used for the
analyses and their data combined. The improvement in the percent
bias standard deviation between the analyses provided by the SSP
function was about 10%, with an additional improvement in
measurement performance arising from the mean percent bias moving
closer to zero (-0.011 vs. 0.043). Preferably, the SSP function
provides an at least 5%, more preferably an at least 8%,
improvement in the percent bias standard deviation for five
different lots of test sensors.
Table 3, below, summarizes the individual lot performances. For
each lot of test sensors, an improvement in measurement performance
arises from the reduction in percent bias standard deviation, the
mean percent bias moving closer to zero, or both.
TABLE-US-00003 TABLE 3 Measurement performance of individual test
sensor lots Lot#1 Lot#2 Lot#3 Lot#4 Lot#5 Overall Conversion + Mean
% 0.049 0.029 0.062 0.111 -0.039 0.042 Primary bias % bias SD 0.332
0.258 0.317 0.238 0.215 0.276 Conversion + Mean % -0.044 -0.056
0.068 -0.002 -0.019 -0.011 Primary + SSP bias % bias SD 0.299 0.225
0.261 0.242 0.190 0.246
FIG. 4A depicts the output signals from an electrochemical
amperometric analysis when two relatively long excitations
separated by a relatively long relaxation are applied to a sample
of blood containing glucose. Such an analysis may be performed on a
blood sample using a measurement device and a test sensor. The
sample of blood included 100 mg/dL of glucose and included 40%
(weight/weight) hematocrit. The first excitation of the input
signal generated output currents 1, while the second excitation of
the input signal generated output currents 2. The first excitation
is not used to determine the concentration of the analyte (glucose)
in the sample (blood), but primarily functions to oxidize mediator
that has undergone reduction during storage of the test sensor. The
final current of the output currents 2 (at 30 seconds) is the
end-point reading and is used with a conversion function to
determine the analyte concentration of the sample. The analysis was
performed at approximately 25.degree. C.
FIG. 4B shows the dose response lines when this analysis was
performed on multiple blood samples at approximately 25.degree. C.,
but with hematocrit contents of 20%, 40%, and 60% and glucose
concentrations from 0 to 700 mg/dL. For each analysis, the analyte
concentration of the sample was directly determined from the
end-point reading of the second excitation, thus at 30 seconds in
relation to FIG. 4A. As may be seen in the divergence between the
lines, the hematocrit effect can result in up to .+-.30% bias
verses the reference concentration as determined with a YSI
reference instrument in plasma.
The output currents from the first and second excitations were
segmented. The output currents from the first excitation were
divided into the following segments:
Segment 1 (designated as "0.9"): data points 1 through 3. These
data points were measured within 0.9 seconds of the application of
the input signal to the sample, with a data point measured at 0.3
second intervals. This Segment included a total of 3 data
points.
Segment 2 (designated as "1.8"): data points 4 through 6. Data
point 1.8 represents the 6.sup.th data point measured and is the
last data point included in this segment. Thus, Segment 2 includes
data points recorded after the 0.9 second recorded data point
(which is included in Segment 1) up to and including the data point
recorded at 1.8 seconds from the initial application of the input
signal to the sample. This Segment included a total of 3 data
points.
Segment 3 (designated as "2.7"): data points 7 through 9. This
Segment included a total of 3 data points.
Segment 4 (designated as "3.6"): data points 10 through 12. This
Segment included a total of 3 data points.
Segment 5 (designated as "4.8"): data points 13 through 16. This
Segment included 4 data points.
Segment 6 (designated as "6"): data points 17 through 20. This
Segment included 4 data points.
Segment 7 (designated as "7.2"): data points 21 through 24. This
Segment included 4 data points.
Segment 8 (designated as "8.4"): data points 25 through 28. This
Segment included 4 data points.
Segment 9 (designated as "9.9"): data points 30 through 33. This
Segment included 4 data points.
An irregular segmenting interval was used to segment the output
signals from the two input excitations. The segmenting interval
started at 0.9 second (Segment 1 to Segment 4), increased to 1.2
second (Segment 5 to Segment 8), and ended with a 1.5 second
interval (Segment 9). As the decay in the output signal currents
became shallower, a relatively longer segmenting interval was used
to provide better definition to the resulting SSP parameters. Thus,
segmenting intervals that increase the definition between the SSP
parameters are preferred.
As the first excitation is not used to determine the concentration
of the analyte in the sample, the second excitation was segmented
and processed similarly to a continuous output signal as previously
described. The output currents from the second excitation were
similarly divided into the following segments: 20.9, 21.8, 22.7,
23.6, 24.8, 26, 27.2, 28.4 and 29.9. The same irregular segmenting
intervals were used to segregate the output currents from the
second excitation.
The output signal segments were then processed to provide SSP
parameters. The normalized differential method was used to process
the output signal segments into SSP parameters by obtaining the
differential between the first and the last data point (current
value) for each segment, followed by normalization with the
end-point reading of the continuous output signal measured at 29.9
seconds. FIG. 4C plots the differentials of each output signal
segment normalized by the end-point reading of the second
excitation. For example, the "9.9" segment was determined with
(i.sub.9sec-i.sub.9.9sec)/i.sub.29.9sec and the "20.9" segment was
determined with (i.sub.20.3sec-i.sub.20.9sec)/i.sub.29.9sec.
FIG. 4D plots the differentials of each output signal segment
normalized by the end-point reading of the excitation from which
the segment values were recorded. For example, using segment
normalized differentials, the "9.9.sub.snd"
segment=(i.sub.9sec-i.sub.9.9sec)/i.sub.9.9sec, where the 9.9
second current value is the last current value recorded from the
first input excitation, and the "20.9.sub.snd"
segment=(i.sub.20.3sec-i.sub.20.9sec)/i.sub.29.9sec, where the 29.9
second current value is the last current value recorded from the
second input excitation.
FIG. 4E plots the time-based differentials of each output signal
segment normalized by the end-point reading of the excitation from
which the segment values were recorded. For instance, the
time-based normalized differential may be represented by
"9.9.sub.tnd"=(i.sub.9sec-i.sub.9.9sec)/(9 s-9.9 s)/i.sub.9.9sec
and "20.9.sub.tnd"=(i.sub.20.3sec-i.sub.20.9sec)/(20.3 s-20.9
s)/i.sub.29.9sec. These are time gradients (currents divided by
time) within each segment with normalization by the segment
end-point reading. Other methods may be used to process the output
signal segments.
Once processed into SSP parameters, multiple SSP parameters, error
parameters, and values representing the uncompensated analyte
concentration of the sample may be considered as terms for
potential inclusion in the complex index function, which served as
the SSP function. Table 4, below, lists the weighing coefficients
selected in view of the exclusion test/s from a multi-variable
regression of SSP parameters, error parameters, and the
uncompensated glucose concentration determined from end-point
current 2 of the second excitation, as represented in FIG. 4A.
MINITAB version 14 software was used with the Multi-Variant
Regression of Linear Combinations of Multiple Variables option
chosen to perform the multi-variable regression. Other statistical
analysis or regression options may be used to determine the
weighing coefficients for the terms.
TABLE-US-00004 TABLE 4 Results of two excitation multivariable
regression. Weighing Terms Coefficients 6 0.64347 8.4 0.9601 20.9
42.281 21.8 -170.670 23.6 -8.0624 28.4 80.595 G 0.0028633 R2/1
12.143 R2 8.825 0.9*G -0.0009523 20.9*G 0.016148 21.8*G -0.067240
27.2*G -0.039550 R2/1*G -0.0043275 20.9*R2/1 -64.138 21.8*R2/1
271.09 28.4*R2/1 -116.44
The resulting complex index function which served as the SSP
function may be represented as follows: SSP
Function=-12.384+0.64347*`6`+0.9601*`8.4`+42.281*`10.8`-170.67*`11.7`-8.0-
624*`13.5`+80.595*`18.3`+0.002863*`G`+12.143*`R2/1`+8.825*`R2`-0.0009523*`-
0.9*G`+0.016148*`20.9*G`-0.06724*`21.8*G`-0.03955*`28.2*G`-0.0043275*`R2/1-
*G`-64.138*`20.9*R2/1`+271.09*`21.8*R2/1`-116.44*`28.4*R2/1` where
G is the uncompensated glucose concentration of the sample, R2/1 is
the end-point reading of the output from the second excitation over
the end-point reading of the output from the first excitation, and
R2 is the end-point reading of the output from the second
excitation over the initial reading of the output from the second
excitation. The SSP function will generate a value from all
parameters within the function, which represents the system total
error in the form of .DELTA.S/S. Thus,
G.sub.comp=(i.sub.raw-Int)/[(S.sub.cal*(1+SSP))] as the hematocrit
compensated glucose value, where i.sub.raw is the output signal
value used to determine the analyte concentration of the sample and
Int may be 0.
FIG. 4F compares the total relative error (.DELTA.G/G) of the
uncompensated and SSP function compensated analyte concentrations
determined from multiple blood samples including from 20% to 60%
(volume/volume) hematocrit and glucose concentrations from
approximately 50 to 700 mg/dL at approximately 25.degree. C. As
shown in the figure, a reduction in relative error of approximately
50% was provided when the SSP function provided primary
compensation. Preferably, the SSP function provides a determined
analyte concentration with 30% less, more preferably 40% less, and
even more preferably 50% less, relative error than the
uncompensated analyte compensation determined from the output
signal and the conversion function.
FIG. 5A depicts the input signals applied to the test sensor for an
electrochemical gated amperometric analysis where six relatively
short excitations are separated by five relaxations of varying
duration. In addition to the six excitations applied to the working
and counter electrodes, a second input signal is applied to an
additional electrode to generate a secondary output signal. The
input signal was applied to the additional electrode after
completion of the analytic input signal applied between the working
and counter electrodes, but may be applied at other times. The
input signal applied to the additional electrode included a seventh
higher voltage pulse. The solid lines describe the substantially
constant input potentials, while the superimposed dots indicate
times of taking current measurements. This input signal was applied
to multiple test sensors used to determine the glucose
concentration of blood from multiple internal clinical studies.
Such an analysis may be performed on a blood sample using a
measurement device and a test sensor.
The excitations of the analytic input signal of FIG. 5A included
pulse-widths of about 0.2, about 0.4, and about 0.5 seconds. While
other pulse-widths may be used, pulse widths from about 0.1 to
about 0.5 seconds are preferred. Pulse-widths greater than 2
seconds are less preferred. The analytic excitations are separated
by relaxations of about 0.5 and about 1 second and were provided by
open circuits. While other relaxation-widths may be used,
relaxation-widths from about 0.3 to about 1.5 seconds are
preferred. The relaxation-width directly preceding the excitation
including the current measurement from which the concentration of
the analyte is determined is preferably less than 1.5 second.
Relaxation-widths greater than 5 seconds are less preferred. In
addition to open circuits, relaxations may be provided by other
methods that do not apply a potential that appreciably causes the
analyte and/or mediator to undergo an electrochemical redox
reaction. Preferably, the application of the analytic input signal
and the measurement of the associated output currents from the
sample are complete in seven seconds or less.
A secondary output signal in the form of a current from an
additional electrode may be considered an error parameter
describing the hematocrit content of a blood sample. The hematocrit
content of the sample may be considered an error parameter because
an error in concentration values may arise from performing an
analysis at a hematocrit content other than that at which the
reference correlation was determined. The hematocrit content of the
sample may be determined from any source, such as an electrode,
calculated estimates, and the like.
FIG. 5B depicts the output current values recorded from the six
amperometric excitations and the secondary output signal. SSP
parameters were determined from these output signals by normalizing
the differential of each segmented signal by the current i.sub.5,4,
which is used to represent the end-point reading of the analysis.
The i.sub.5,4 current was used to represent the end-point reading,
as of the multiple current values recorded, this current reading
best described the analyte concentration of the sample. While
another value could be selected as the end-point reading for
normalization, preferably the end-point reading used for
normalization is that which correlates best with the underlying
analyte concentration of the sample.
The output currents from the individual excitations were segmented
and converted to SSP parameters as follows:
d12=(i.sub.1,1-i.sub.1,2)/i.sub.5,4,
d13=(i.sub.1,2-i.sub.1,3)/i.sub.5,4,
d14=(i.sub.1,3-i.sub.1,4)/i.sub.5,4,
d15=(i.sub.1,4-i.sub.1,5)/i.sub.5,4, . . . . The output currents
from the secondary output signal were normalized by i.sub.7,4. The
SSP parameters determined from FIG. 5B were d12, d13, d14, d15,
d22, d32, d33, d34, d42, d43, d44, d52, d53, d54, d62, d63, d64,
d72, d73, d74. Other SSP parameters may be used.
The remaining residual error (RRE) present after compensation by
the primary and first residual functions may be generally
represented by: dG/G_1=(G.sub.comp1-G.sub.ref)/G.sub.ref. Once
processed into SSP parameters, the multiple SSP parameters,
cross-terms of the SSP parameters, and values representing the
uncompensated analyte concentration of the sample may be considered
as terms for potential inclusion in the complex index function,
which served as the SSP function. Table 5, below, lists the
weighing coefficients selected in view of the exclusion test/s
resulting from a multi-variable regression. MINITAB version 14
software was used with the Multi-Variant Regression of Linear
Combinations of Multiple Variables option chosen to perform the
multi-variable regression. Other statistical analysis or regression
options may be used to determine the weighing coefficients for the
terms.
TABLE-US-00005 TABLE 5 Results of multi-excitation multivariable
regression. Weighing Terms Coefficients Temp 0.011077 d12 0.11892
d22 -0.19642 d33 -14.314 d34 18.401 d42 0.30470 d63 4.8410 d73
2.5512 d15G -0.0021700 d64G -0.0068789 d72G 0.009718 7d13
-0.00030004 7d33 0.0074282 7d34 -0.009218 7d53 -0.0018402 d22d54G
0.049078 d62d72G -0.014893 7d22G -0.00000218
The resulting complex index function which served as the SSP
function may be represented as follows: SSP Function=-0.3161
9-0.011077*`T`+0.1189*`d12`-0.1
964*`d22`-14.31*`d33`+18.4*`d34`+0.3047*`d42`+4.841*`d63`+2.551*`d73`-0.0-
0217*`D15G`-0.006879*`d64G`+0.009718*`d72G`-0.0003*`7d13`+0.007428*`7d33`--
0.009218*`7d34`-0.00184*`7d53`+0.04908*`d22d54G`-0.01489*`d62d72G`-2.18e-6-
*`7d22G` where G is the uncompensated glucose concentration of the
sample, T is temperature, 7d13 is an example of a cross-term formed
by the end-point reading of seventh pulse times d13, and d22d54G is
an example of a cross-term formed by multiplying d22, d54, and
G.
Analyses were performed using four different manufacturing lots of
test sensors to perform approximately 158 analyses. Approximately
79 of these analyses were from HCP-testing while the remaining
approximately 79 analyses arose from user self-testing. Biosensor
test sensors vary from lot-to-lot in their ability to reproducibly
produce the same output signal in response the same input signal
and sample analyte concentration. While preferable to equip the
measurement device with a single reference correlation for the
conversion function, doing so limits the manufacturing variance
that can occur between different lots of test sensors.
FIG. 6A is a correlation plot comparing the total error to the
predicted error of the analyte concentrations determined using only
the primary function. FIG. 6B is a correlation plot comparing the
total error to the predicted error of the analyte concentrations
determined using the primary and first residual functions. FIG. 6C
is a correlation plot comparing the total error to the predicted
error of the analyte concentrations determined using the primary,
first residual, and SSP functions.
Progressive improvements in measurement performance were observed
from the first residual function and the SSP function in relation
to primary function compensation alone. This was especially the
case for the scattered data points. The improvement can be seen in
the progressive reduction of the percent bias standard deviation
term S (SD value, 0.0518, 0.0423, 0.0314) with respect to the
regression line of the total error (dG/G), or the increase of the
correlation coefficient R.sup.2 values (71.7%, 81.1% and
89.6%).
Thus, the compensated analyte concentration may be generally
determined with the relationship (concentration determined from
primary and first residual compensation)/(1+SSP function). FIG. 6D
and FIG. 6E compare the compensation results from primary+first
residual and additional compensation with the SSP function. In FIG.
6D, the %-bias is expressed in pure percent, that is,
%-bias=100%.times.(G.sub.final-G.sub.ref)/G.sub.ref with expanded
boundary.+-.100%.times.(10/Gref) after 100 mg/dL. In FIG. 6E, the
%-bias is expressed pure percent for G.gtoreq.2100 mg/dL, and bias
(G.sub.final-G.sub.ref) for G<100 mg/dL with fixed boundary of
.+-.10%. These two expressions are equivalent, but FIG. 6D more
readily shows the improvement in measurement performance in the low
glucose region with the addition of SSP function compensation.
FIG. 7A represents the input signal applied to the working and
counter electrodes of a test sensor for an electrochemical combined
gated amperometric and gated voltammetric analysis. The input
signal included two amperometric excitations followed by five
voltammetric excitations. The excitations were separated by six
relaxations of varying duration. The dashed lines represent the
input signal and show that the amperometric excitations were
applied at a substantially constant voltage/potential, while the
voltammetric excitations are triangular in shape, thus having a
potential that changes with time. In this example, the voltage scan
rate was 0.5 V/second for the voltammetric excitations, although
other scan rates may be used. The output currents measured from the
sample for each excitation in micro amps (uA) are represented by
the corresponding solid lines. Output current values were recorded
about every 10 milliseconds for each voltammetric excitation. While
the amperometric excitations produced a continuous decay, the
voltammetric excitations provided a two-step decay with respect to
time from the forward and reverse portion of each voltammetric
excitation. Such an analysis may be performed on a blood sample
using a measurement device and a test sensor.
The amperometric excitations of the input signal of FIG. 7A have
pulse-widths of about 0.5 and 0.25 seconds. The voltammetric
excitations of the analytic input signal included pulse-widths of
about 0.4 seconds. While other pulse-widths may be used, pulse
widths from about 0.1 to about 0.5 seconds are preferred.
Pulse-widths greater than 2 seconds are less preferred. Preferably,
the scan range of the voltammetric excitation from which the
analyte concentration of the sample is determined is within the
plateau range of the measurable species so that the electrochemical
redox reaction of the measurable species is substantially diffusion
limited.
The voltammetric analytic excitations were separated by relaxations
of about 1 second and were provided by open circuits. While other
relaxation-widths may be used, relaxation-widths from about 0.3 to
about 1.5 seconds are preferred. The relaxation-width directly
preceding the excitation including the current measurement from
which the concentration of the analyte was determined is preferably
less than 1.5 second. Relaxation-widths greater than 3 seconds are
less preferred. In addition to open circuits, relaxations may be
provided by other methods that do not apply a potential that
appreciably causes the analyte and/or mediator to undergo an
electrochemical redox reaction during the relaxation. Preferably,
the application of the analytic input signal and the measurement of
the associated output currents from the sample are complete in
eight seconds or less.
FIG. 7B shows the currents obtained for multiple analyses from the
third voltammetric excitation of the seven excitation input signal
having two amperometric and five voltammetric excitations. The
analyses were performed on blood samples including about 80 mg/dL
of glucose as the analyte and 25%, 40%, or 55% hematocrit by
volume. Table 6, below shows the time from the application of the
input signal to the sample and the time within the pulse for the
output signal current value recorded from the third voltammetric
excitation.
TABLE-US-00006 TABLE 6 Output signal measured current values Time
from input signal application, Time within pulse, Measured sec.
sec. Current, uA. 4.81 0.01 10.05638 4.86 0.06 5.94202 4.91 0.11
4.706399 5 0.2 3.766113 5.01 0.21 3.57111 5.11 0.31 2.729612 5.2
0.4 2.208661
FIG. 7C shows the currents obtained from the third voltammetric
excitation when the blood samples included about 400 mg/dL glucose.
As may be seen in the figure, the hematocrit content of the sample
had a larger effect on the output currents for the higher glucose
concentration blood samples.
FIG. 7D represents how the output currents from the third
voltammetric excitation were segmented to provide three output
signal segments "4.8", "4.85", and "5" from the excitation. The
segments were labeled with the time after initiation of the input
signal corresponding to the first current value of each
segment.
In this example, the output currents from the five gated
voltammetric excitations were segmented into two segments for the
forward portion of the excitation and into one segment for the
reverse portion of the excitation. Thus, three SSP parameters were
determined from each gated voltammetric excitation. Additional SSP
parameters may be calculated from one or more of the excitations
for either the forward or reverse portions of the excitation.
SSP parameters were then determined from the output currents from
the third voltammetric excitation. While other SSP parameter
determining methods may be used, each of the previously described
methods were used to provide three SSP parameters "4.8", "4.85",
and "5" for the third voltammetric excitation as in Table 7,
below.
TABLE-US-00007 TABLE 7 SSP Parameter Determination Nml SSP Par. Avg
Ratio Diff Diff TD TnD Decay K Decay R `4.8` 7.9992 0.5908 4.114
1.862 82.287 37.256 0.293 0.006 `4.85` 4.8540 0.6338 2.175 0.985
43.518 7.036 0.378 0.039 `5` 2.8898 0.6184 1.362 0.616 15.138 3.246
0.745 0.212
To perform the compensation, SSP parameters were determined from
the segments from the remaining voltammetric excitations using the
time-based normalized differential SSP parameter generation method
by normalizing the differential of each segmented signal by the
current i.sub.5.2, which represented the end-point reading of the
third excitation and was measured at 5.2 seconds after the
initiation of the application of the input signal to the sample.
For this gated input signal, the output signals from each
excitation were normalized with the end-point reading of the
excitation. Thus, three SSP parameters were determined from each of
the five voltammetric excitations represented in FIG. 7A. If the
analysis end-point, as opposed to each intermediate end-point from
the excitations had been used to determine the SSP parameters, is
would have been the normalization value.
Thus, the time-based normalized differential SSP parameter
generation method was used, [.DELTA.i/(-.DELTA.t)/i.sub.EP], where
the i.sub.EP value used for normalization was the end-point current
of each excitation. The output currents from the individual
voltammetric excitations were segmented and converted to SSP
parameters as follows:
4.8=(i.sub.4.81-i.sub.4.86)/(4.86-4.81)/i.sub.5.2,
4.85=(i.sub.4.86-i.sub.5)/(5-4.86)/i.sub.5.2, and
5=(i.sub.5.01-i.sub.5.2)/(5.2-5.01)/i.sub.5,2, as an example. This
general method was applied to the output currents from the five
voltammetric excitations of FIG. 7A to produce the SSP parameters
as in Table 8, below.
TABLE-US-00008 TABLE 8 SSP Parameters from Gated Voltammetric
Excitations Voltammetric Excitation SSP Parameters 3 "2.0" =
(i.sub.2.01 - i.sub.2.06)/(2.06 - 2.01)/i.sub.2.4 "2.05" =
(i.sub.2.06 - i.sub.2.2)/(2.2 - 2.06)/i.sub.2.4 "2.2" = (i.sub.2.21
- i.sub.2.4)/(2.4 - 2.21)/i.sub.2.4 4 "3.4" = (i.sub.3.41 -
i.sub.3.46)/(3.46 - 3.41)/i.sub.3.8 "3.45" = (i.sub.3.46 -
i.sub.3.6)/(3.6 - 3.46)/i.sub.3.8 "3.6" = (i.sub.3.61 -
i.sub.3.8)/(3.8 - 3.61)/i.sub.3.8 5 "4.8" = (i.sub.4.81 -
i.sub.4.86)/(4.86 - 4.81)/i.sub.5.2 "4.85" = (i.sub.4.86 -
i.sub.5)/(5 - 4.86)/i.sub.5.2 "5" = (i.sub.5.01 - i.sub.5.2)/(5.2 -
5.01)/i.sub.5.2 6 "6.2" = (i.sub.6.21 - i.sub.6.26)/(6.26 -
6.21)/i.sub.6.6 "6.25" = (i.sub.6.26 - i.sub.6.4)/(6.4 -
6.26)/i.sub.6.6 "6.4" = (i.sub.6.41 - i.sub.6.6)/(6.6 -
6.41)/i.sub.6.6 7 "7.6" = (i.sub.7.61 - i.sub.7.66)/(7.66 -
7.61)/i.sub.8 "7.65" = (i.sub.7.66 - i.sub.7.8)/(7.8 -
7.626)/i.sub.8 "7.8" = (i.sub.7.81 - i.sub.8)/(8 -
7.81)/i.sub.8
A complex index function determined from these SSP parameters to
provide a SSP function may be represented as follows: SSP
Function=-1.4137-0.0059269*`2.0`-0.38649*`2.05`+1.605*`2.2`-2.3567*`3.6`+-
2.1962*`4.85`-1.9223*`6.25`+0.87157*`6.4`+0.27137*`7.65`-0.00021187*`2G`-0-
.0039181*`2.2G`+0.00026258*`3.4G`+0.0064633*`3.45G`+0.0037505*`3.6G`-0.014-
191*`4.85G`+0.0078856*`6.25G` where G is the uncompensated glucose
concentration of the sample and "2.0"*G is an example of a
cross-term formed by the product of the "2.0" SSP parameter and the
uncompensated glucose concentration of the sample.
The uncompensated glucose concentration of the sample was
determined with the general relationship
G=(i.sub.5.2-Int)/S.sub.cal, where i.sub.5.2 is the current value
measured after 5.2 seconds of initiating the input signal from the
third gated voltammetric excitation, Int is the intercept of a
reference correlation, which may be 0, and S.sub.cal is the
reference correlation relating output currents from the measurement
device to known sample analyte concentrations as determined with a
reference instrument. In this example, the end-point current of the
third voltammetric excitation was used to determine the analyte
concentration of the sample; however, an intermediate current from
within an excitation also may be used to determine the analyte
concentration of the sample. Table 9 below shows how a sample
analyte concentration was determined from both an intermediate
current at 5.0 seconds and from the 5.2 second end-point current of
the third voltammetric excitation. The slopes and intercepts in
Table 9 were predetermined from regressions of multiple current
readings at multiple glucose levels.
TABLE-US-00009 TABLE 9 Intermediate and End-Point Current
Concentrations G_5.0, G_5.2, YSI, mg/dL i_5.0, uA i_5.2, uA mg/dL
mg/dL % bias_5.0 % bias_5.2 79.2 1.71 1.14 83.81 80.01 5.8 1.0
170.5 3.61 2.61 170.29 172.18 -0.1 1.0 278.5 5.88 4.34 273.66
280.25 -1.7 0.6 452.0 9.90 7.12 457.29 455.06 1.2 0.7 Slope.sub.RC
0.0219 0.0159 Intercept.sub.RC -0.1279 -0.1333
The reference analyte concentrations for the samples were
determined with a YSI reference instrument. The slope and intercept
values for the reference correlation were previously determined for
a blood sample including a known glucoses concentration of 175
mg/dL and a hematocrit content of 40%. The output current values
recorded for the samples at 5.0 seconds and at 5.2 seconds were
used with the reference correlation to determine the sample analyte
concentrations. The percent biases for the determined analyte
concentrations were determined in relation to the reference analyte
concentrations.
While compensation may be used in addition to the SSP function for
gated voltammetric input signals, in this example the SSP function
was used to provide primary compensation generally in accord with
FIG. 2B using the general relationship G.sub.comp=G/(1+SSP
Function), where G.sub.comp is the SSP parameter compensated
analyte concentration of the sample. Either the G_5.0 or the G_5.2
determined analyte concentrations from Table 7 may be compensated
in this way. The previously discussed SSP compensation methods also
may be used with analyte concentrations determined in these
ways.
FIG. 7E shows the currents measured at 5.2 seconds from the third
gated voltammetric excitation for blood samples including about 80
mg/dL, 170 mg/dL, 275 mg/dL, or 450 mg/dL glucose with hematocrit
levels of 25%, 40%, or 55% by volume. As can be seen from the
graph, there is greater divergence from the 40% Hct line by the 25%
and 55% Hct samples at higher glucose concentrations. The reference
glucose concentration of the samples was determined with a YSI
reference instrument in the laboratory.
FIG. 7F shows the glucose readings obtained from the measurement
device with and without compensation provided by the SSP function.
The uncompensated analyte concentration (G) of each sample was
determined with the general relationship
G=(i.sub.5.2-Int)/S.sub.cal, where Int and S.sub.cal are from a
reference correlation determined in the laboratory with a YSI
reference instrument from multiple analyses. The compensated
analyte concentration (G_comp) of each sample was determined with
the general relationship G.sub.comp=G/(1+SSP Function). As seen in
the figure, the compensated analyte concentrations are more closely
grouped for the different analyte concentrations and Hct
volumes.
FIG. 7G compares the relative error between the determined SSP
compensated and uncompensated glucose analyte concentrations for
the blood samples. Even at high glucose concentration, the SSP
compensated determined analyte concentrations are close to the 0
error line, especially in comparison to the uncompensated
determined analyte concentrations. The percent bias standard
deviation for the uncompensated determined analyte concentrations
was 13.5% while that for the SSP function compensated determined
analyte concentrations was 5.9%. Thus, the SSP function
compensation provided an approximately 56% (13.5-5.9/13.5*100)
reduction in relative error in comparison to the analyte
concentrations determined without SSP compensation.
FIG. 8 depicts a schematic representation of a biosensor system 800
that determines an analyte concentration in a sample of a
biological fluid. Biosensor system 800 includes a measurement
device 802 and a test sensor 804. The measurement device 802 may be
implemented in any analytical instrument, including a bench-top
device, a portable or hand-held device, or the like. The
measurement device 802 and the test sensor 804 may be adapted to
implement an electrochemical sensor system, an optical sensor
system, a combination thereof, or the like.
The biosensor system 800 determines the analyte concentration of
the sample from a method of error compensation including at least
one conversion function, at least one SSP function, and the output
signal. The method of error compensation may improve the
measurement performance of the biosensor system 800 in determining
the analyte concentration of the sample. The biosensor system 800
may be utilized to determine analyte concentrations, including
those of glucose, uric acid, lactate, cholesterol, bilirubin, and
the like. While a particular configuration is shown, the biosensor
system 800 may have other configurations, including those with
additional components.
The test sensor 804 has a base 806 that forms a reservoir 808 and a
channel 810 with an opening 812. The reservoir 808 and the channel
810 may be covered by a lid with a vent. The reservoir 808 defines
a partially-enclosed volume. The reservoir 808 may contain a
composition that assists in retaining a liquid sample such as
water-swellable polymers or porous polymer matrices. Reagents may
be deposited in the reservoir 808 and/or the channel 810. The
reagents may include one or more enzymes, binders, mediators, and
like species. The reagents may include a chemical indicator for an
optical system. The test sensor 804 may have other
configurations.
In an optical sensor system, the sample interface 814 has an
optical portal or aperture for viewing the sample. The optical
portal may be covered by an essentially transparent material. The
sample interface 814 may have optical portals on opposite sides of
the reservoir 808.
In an electrochemical system, the sample interface 814 has
conductors connected to a working electrode 832 and a counter
electrode 834 from which the analytic output signal may be
measured. The sample interface 814 also may include conductors
connected to one or more additional electrodes 836 from which
secondary output signals may be measured. The electrodes may be
substantially in the same plane or in more than one plane. The
electrodes may be disposed on a surface of the base 806 that forms
the reservoir 808. The electrodes may extend or project into the
reservoir 808. A dielectric layer may partially cover the
conductors and/or the electrodes. The sample interface 814 may have
other electrodes and conductors.
The measurement device 802 includes electrical circuitry 816
connected to a sensor interface 818 and an optional display 820.
The electrical circuitry 816 includes a processor 822 connected to
a signal generator 824, an optional temperature sensor 826, and a
storage medium 828.
The signal generator 824 provides an electrical input signal to the
sensor interface 818 in response to the processor 822. In optical
systems, the electrical input signal may be used to operate or
control the detector and light source in the sensor interface 818.
In electrochemical systems, the electrical input signal may be
transmitted by the sensor interface 818 to the sample interface 814
to apply the electrical input signal to the sample of the
biological fluid. The electrical input signal may be a potential or
current and may be constant, variable, or a combination thereof,
such as when an AC signal is applied with a DC signal offset. The
electrical input signal may be applied continuously or as multiple
excitations, sequences, or cycles. The signal generator 824 also
may record an output signal from the sensor interface as a
generator-recorder.
The optional temperature sensor 826 determines the temperature of
the sample in the reservoir of the test sensor 804. The temperature
of the sample may be measured, calculated from the output signal,
or presumed to be the same or similar to a measurement of the
ambient temperature or the temperature of a device implementing the
biosensor system. The temperature may be measured using a
thermister, thermometer, or other temperature sensing device. Other
techniques may be used to determine the sample temperature.
The storage medium 828 may be a magnetic, optical, or semiconductor
memory, another storage device, or the like. The storage medium 828
may be a fixed memory device, a removable memory device, such as a
memory card, remotely accessed, or the like.
The processor 822 implements the analyte analysis and data
treatment using computer readable software code and data stored in
the storage medium 828. The processor 822 may start the analyte
analysis in response to the presence of the test sensor 804 at the
sensor interface 818, the application of a sample to the test
sensor 804, in response to user input, or the like. The processor
822 directs the signal generator 824 to provide the electrical
input signal to the sensor interface 818. The processor 822
receives the sample temperature from the temperature sensor 826.
The processor 822 receives the output signal from the sensor
interface 818. The output signal is generated in response to the
reaction of the analyte in the sample. The output signal may be
generated using an optical system, an electrochemical system, or
the like. The processor 822 determines analyte concentrations from
output signals using a compensation method including a conversion
function and at least one SSP function as previously discussed.
Once the desired segments are determined for the biosensor system,
they may be implemented as the segmenting routine in the
measurement device. The processor 822 selects which values of the
output signal to process for two or more segments for SSP parameter
processing based on a predetermined segmenting routine as stored in
the storage medium 828. The results of the analyte analysis may be
output to the display 820, a remote receiver (not shown), and/or
may be stored in the storage medium 828.
The reference correlation between reference analyte concentrations
and output signals from the measurement device 802 and other
correlations, such as index functions, may be represented
graphically, mathematically, a combination thereof, or the like.
Correlation equations may be represented by a program number (PNA)
table, another look-up table, or the like that is stored in the
storage medium 828. Constants and weighing coefficients also may be
stored in the storage medium 828.
Instructions regarding implementation of the analyte analysis also
may be provided by the computer readable software code stored in
the storage medium 828. The code may be object code or any other
code describing or controlling the functionality described herein.
The data from the analyte analysis may be subjected to one or more
data treatments, including the determination of decay rates, K
constants, ratios, functions, and the like in the processor
822.
In electrochemical systems, the sensor interface 818 has contacts
that connect or electrically communicate with the conductors in the
sample interface 814 of the test sensor 804. The sensor interface
818 transmits the electrical input signal from the signal generator
824 through the contacts to the connectors in the sample interface
814. The sensor interface 818 also transmits the output signal from
the sample through the contacts to the processor 822 and/or signal
generator 824.
In light-absorption and light-generated optical systems, the sensor
interface 818 includes a detector that collects and measures light.
The detector receives light from the liquid sensor through the
optical portal in the sample interface 814. In a light-absorption
optical system, the sensor interface 818 also includes a light
source such as a laser, a light emitting diode, or the like. The
incident beam may have a wavelength selected for absorption by the
reaction product. The sensor interface 818 directs an incident beam
from the light source through the optical portal in the sample
interface 814. The detector may be positioned at an angle such as
45.degree. to the optical portal to receive the light reflected
back from the sample. The detector may be positioned adjacent to an
optical portal on the other side of the sample from the light
source to receive light transmitted through the sample. The
detector may be positioned in another location to receive reflected
and/or transmitted light.
The optional display 820 may be analog or digital. The display 820
may include a LCD, a LED, an OLED, a vacuum fluorescent, or other
display adapted to show a numerical reading. Other display
technologies may be used. The display 820 electrically communicates
with the processor 822. The display 820 may be separate from the
measurement device 802, such as when in wireless communication with
the processor 822. Alternatively, the display 820 may be removed
from the measurement device 802, such as when the measurement
device 802 electrically communicates with a remote computing
device, medication dosing pump, and the like.
In use, a liquid sample for analysis is transferred into the
reservoir 808 by introducing the liquid to the opening 812. The
liquid sample flows through the channel 810, filling the reservoir
808 while expelling the previously contained air. The liquid sample
chemically reacts with the reagents deposited in the channel 810
and/or reservoir 808.
The test sensor 802 is disposed in relation to the measurement
device 802, such that the sample interface 814 is in electrical
and/or optical communication with the sensor interface 818.
Electrical communication includes the transfer of input and/or
output signals between contacts in the sensor interface 818 and
conductors in the sample interface 814. Optical communication
includes the transfer of light between an optical portal in the
sample interface 814 and a detector in the sensor interface 818.
Optical communication also includes the transfer of light between
an optical portal in the sample interface 814 and a light source in
the sensor interface 818.
The processor 822 directs the signal generator 824 to provide an
input signal to the sensor interface 818. In an optical system, the
sensor interface 818 operates the detector and light source in
response to the input signal. In an electrochemical system, the
sensor interface 818 provides the input signal to the sample
through the sample interface 814. The processor 822 receives the
output signal generated in response to the redox reaction of the
analyte in the sample as previously discussed.
The processor 822 determines the analyte concentration of the
sample from the output signals using a compensation system
including a conversion function and at least one SSP function. The
processor 822 also may implement primary and/or residual functions
in the compensation system. Other compensations and functions also
may be implemented by the processor 822.
While various embodiments of the invention have been described, it
will be apparent to those of ordinary skill in the art that other
embodiments and implementations are possible within the scope of
the invention.
* * * * *
References